## Monthly Seminar on Arithmetic of Automorphic Forms

Seminar information archive ～06/07｜Next seminar｜Future seminars 06/08～

Date, time & place | Saturday 13:30 - 16:00 123Room #123 (Graduate School of Math. Sci. Bldg.) |
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**Seminar information archive**

### 2014/10/11

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The "secondary spherical function" of the discrete series representations of $SU(3,1)$ (following the memo of Tadashi Miyazaki) (JAPANESE)

Toward Fourier expansion of automorphic forms on $Sp(2, R)$ (JAPANESE)

**Takayuki Oda**(Grad. School of Math.-Sci., Univ. of Tokyo) 13:30-14:30The "secondary spherical function" of the discrete series representations of $SU(3,1)$ (following the memo of Tadashi Miyazaki) (JAPANESE)

**Hideshi Takayanagi**(Sakushin-Gakuin University) 15:00-16:00Toward Fourier expansion of automorphic forms on $Sp(2, R)$ (JAPANESE)

### 2014/07/19

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)

種数 3 の trigonal curve から来る Kummer 多様体の定義方程式と Coble の超平面 (JAPANESE)

**Yoshihiro Onishi**(Miejyo University) 13:30-14:30Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)

**Yoshihiro Onishi**(Meijyo University) 15:00-16:00種数 3 の trigonal curve から来る Kummer 多様体の定義方程式と Coble の超平面 (JAPANESE)

### 2014/04/26

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)

Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)

**Ryutarou Okazaki**(Doushisha Univ. until March, 2014) 13:30-14:30The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)

**Ryutarou Okazaki**(Doushisha Univ. until March, 2014) 15:00-16:00Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)

### 2014/02/15

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)

Generalization of Weierstrass P-functions to quasi-Abelian varieties

Canceled for snow storm: (JAPANESE)

**Yoshihiro Oonishi**(Yamanashi Univ.) 13:30-14:30Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)

**Atsuko Kogie**(Toyama Univ.) 15:00-16:00Generalization of Weierstrass P-functions to quasi-Abelian varieties

Canceled for snow storm: (JAPANESE)

### 2014/02/01

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

Minimal submanifolds on type IV symmetric domains (ENGLISH)

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

[ Abstract ]

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00Minimal submanifolds on type IV symmetric domains (ENGLISH)

[ Abstract ]

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/02/01

**Bayarmagnai, G.**(National University of Mongolia) 13:30-14:30

On the three dimensional Whittaker functions on SU(2,2) (ENGLISH)

The speaker will discuss the technical aspect to have explicit Whittaker functions belonging to principal series representations of SU(2,2) with non-trivial minimal K-types.

**Takayuki Oda**(Univ. of Tokyo) 15:00-16:00

Minimal submanifolds on type IV symmetric domains (ENGLISH)

In the explicit constructions of fundamental domains in some typical classical domains with respect standard arithmetic discrete subgroups, there appears real minimal hypersurfaces. But this was known only for real rank one cases. We try to find the situation for the cases of rank 2 by some exapmles.

### 2014/01/11

14:00-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

A product of tensor product L-functions of quasi-split classical groups of Hermitian type. (jointly with Lei Zhang) (ENGLISH)

A product of tensor product L-functions of quasi-split classical groups of Hermitian type, Part II. (jointly with Lei Zhang) (ENGLISH)

**Dihua Jiang**(School of Mathematics, University of Minnesota) 14:00-14:45A product of tensor product L-functions of quasi-split classical groups of Hermitian type. (jointly with Lei Zhang) (ENGLISH)

**Dihua Jiang**(School of Mathematics, University of Minnesota) 15:00-15:45A product of tensor product L-functions of quasi-split classical groups of Hermitian type, Part II. (jointly with Lei Zhang) (ENGLISH)

### 2013/11/16

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Pair correlation of low lying zeros of quadratic L-functions (JAPANESE)

sigam function and space curves (JAPANESE)

**Keijyu SOUNO**(Tokyo University of Agriculture and Technology) 13:30-14:30Pair correlation of low lying zeros of quadratic L-functions (JAPANESE)

[ Abstract ]

In this talk, we give certain asymptotic formula involving non-trivial zeros of L-functions associated to Knonecker symbol under the assumption of the Generalized Riemann Hypothesis. From this formula, we obtain several results on non-trivial zeros of quadratic L-functions near the real axis.

In this talk, we give certain asymptotic formula involving non-trivial zeros of L-functions associated to Knonecker symbol under the assumption of the Generalized Riemann Hypothesis. From this formula, we obtain several results on non-trivial zeros of quadratic L-functions near the real axis.

**Shigeki MATSUTANI**

所属: 相模原(Sagamihara city) 15:30-16:00所属: 相模原

sigam function and space curves (JAPANESE)

[ Abstract ]

In this talk, I show that Kleinian sigma function, which is a generalization of Weierstrass elliptic sigma function, is extended to space curves, (3,4,5), (3,7,8) and (6,13,14,15,16) type. In terms of the function, the Jacobi inversion formula is also generalized, in which the affine coordinates are given as functions of strata of Jacobi variety associated with these curves.

In this talk, I show that Kleinian sigma function, which is a generalization of Weierstrass elliptic sigma function, is extended to space curves, (3,4,5), (3,7,8) and (6,13,14,15,16) type. In terms of the function, the Jacobi inversion formula is also generalized, in which the affine coordinates are given as functions of strata of Jacobi variety associated with these curves.

### 2013/09/10

13:30-15:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Counting automorphic representations (JAPANESE)

Counting automorphic representations II (Sept. 17) (JAPANESE)

**Yuval Flicker**(Ohio State Univ.) 13:30-15:00Counting automorphic representations (JAPANESE)

**Yuval Flicker**(Ohio State University) 13:30-15:00Counting automorphic representations II (Sept. 17) (JAPANESE)

### 2013/06/22

10:00-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

*** (JAPANESE)

*** (JAPANESE)

*******(***) 10:00-11:00*** (JAPANESE)

*******(***) 11:15-12:15*** (JAPANESE)

### 2013/06/22

10:00-12:15 Room #123 (Graduate School of Math. Sci. Bldg.)

On the computation of the ramified Siegel series associated with

trivial character (JAPANESE)

An explicit relative trace formula for Hilbert modular forms and its applications

(JAPANESE)

**Kei-ichi Gunji**(Chiba Inst. Tech) 10:00-11:00On the computation of the ramified Siegel series associated with

trivial character (JAPANESE)

[ Abstract ]

Please check the Japanese version of the web page.

Please check the Japanese version of the web page.

**Masao Tsuzuki**(Sophia University) 11:15-12:15An explicit relative trace formula for Hilbert modular forms and its applications

(JAPANESE)

[ Abstract ]

This is joint work with Shingo Sugiyama. In this talk, we report our recent result on relative trace formula on PGL(2) computing the spectral averages for the central L-values of quadratic base change of holomorphic Hilbert mudular forms. explicitly all local terms of the trace formula, dropping several assumptions which have always been assumed in existing works of similar theme. The following applications of our explicit relative trace formula will be explained:

(i) a spectral equidistribution result in the leve aspect for the Satake parameters weighted by central L-values;

(ii) a subconvexity bound of quadratic base change L-functions for holomorphic Hilbert cusp forms in the weight aspect;

(iii) Existence of infinitely many holomorphic Hilbert cusp forms with arbitrarily large field of definition and with non vanishing central $L$-values.

This is joint work with Shingo Sugiyama. In this talk, we report our recent result on relative trace formula on PGL(2) computing the spectral averages for the central L-values of quadratic base change of holomorphic Hilbert mudular forms. explicitly all local terms of the trace formula, dropping several assumptions which have always been assumed in existing works of similar theme. The following applications of our explicit relative trace formula will be explained:

(i) a spectral equidistribution result in the leve aspect for the Satake parameters weighted by central L-values;

(ii) a subconvexity bound of quadratic base change L-functions for holomorphic Hilbert cusp forms in the weight aspect;

(iii) Existence of infinitely many holomorphic Hilbert cusp forms with arbitrarily large field of definition and with non vanishing central $L$-values.

### 2013/05/11

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Symplectic-orthogonal theta lifts and explicit formulas for archimedean Whittaker functions (JAPANESE)

Infinite product represenation of the Mumford form and its application to the values of Selberg zeta functions (JAPANESE)

**Taku Ishii**(Seikei Univeristy) 13:30-14:30Symplectic-orthogonal theta lifts and explicit formulas for archimedean Whittaker functions (JAPANESE)

**Takashi Ichikawa**(Saga University) 15:00-16:00Infinite product represenation of the Mumford form and its application to the values of Selberg zeta functions (JAPANESE)

### 2013/02/23

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Ramanujan circulant graphs and the Hardy-Littlewood conjecture (JAPANESE)

Generalized Whittaker functions on $G_{2}$ (JAPANESE)

**Miki Hirano**(Ehime University) 13:30-14:30Ramanujan circulant graphs and the Hardy-Littlewood conjecture (JAPANESE)

[ Abstract ]

TBA

TBA

**Hiroaki Narita**(Kumamoto University) 15:00-16:00Generalized Whittaker functions on $G_{2}$ (JAPANESE)

[ Abstract ]

TBA

TBA

### 2012/09/15

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)

Strict positivity of the central values of some Rankin L-functions of GSp(1,1) and special values of hypergeometric functions (JAPANESE)

**Tadashi Miyazaki**(Kitazato University) 13:30-14:30Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)

**Hiro-aki Narita**(Kumamoto University) 15:00-16:00Strict positivity of the central values of some Rankin L-functions of GSp(1,1) and special values of hypergeometric functions (JAPANESE)

[ Abstract ]

We discuss the strict positivity of the central values of certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.

We discuss the strict positivity of the central values of certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.

### 2012/07/21

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On Fourier coefficients of Siegel-Eisenstein series of degree n. (JAPANESE)

Polylogarithms revisited from the viewpoint of the irrationality (JAPANESE)

**S. Takemori**(Kyoto Univ., School of Science) 13:30-14:30On Fourier coefficients of Siegel-Eisenstein series of degree n. (JAPANESE)

[ Abstract ]

We define an Siegel-Eisenstein series G_{k,\\chi} of degree n and talk about an explicit formula of the Fourier coefficients. This Eisenstein series is different from ordinarily defined Eisenstein series E_{k,\\chi}, but if \\chi satisfies a certain condition, we can obtain an explicit formula of Fourier coefficients of E_{k,\\chi}.

We define an Siegel-Eisenstein series G_{k,\\chi} of degree n and talk about an explicit formula of the Fourier coefficients. This Eisenstein series is different from ordinarily defined Eisenstein series E_{k,\\chi}, but if \\chi satisfies a certain condition, we can obtain an explicit formula of Fourier coefficients of E_{k,\\chi}.

**Noriko HIRATA-Kohno**(Nihon University) 15:00-16:00Polylogarithms revisited from the viewpoint of the irrationality (JAPANESE)

[ Abstract ]

In this report, we consider a polylogarithmic function to give a lower bound for the dimension of the linear space over the rationals spanned by $1$ and values of the function. Our proof uses Pad\\'e approximation and a criterion due to Yu. V. Nesterenko. We also describe what happens in the $p$-adic case and in the elliptic one.

In this report, we consider a polylogarithmic function to give a lower bound for the dimension of the linear space over the rationals spanned by $1$ and values of the function. Our proof uses Pad\\'e approximation and a criterion due to Yu. V. Nesterenko. We also describe what happens in the $p$-adic case and in the elliptic one.

### 2012/05/19

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

TBA (JAPANESE)

TBA (JAPANESE)

**Takashi Taniguchi**(Kobe Univeristy) 13:30-14:30TBA (JAPANESE)

**Masao Tsuzuki**(Sophia University) 15:00-16:00TBA (JAPANESE)

### 2012/04/14

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)

Moments of the derivatives of the Riemann zeta function (JAPANESE)

**Kazutoshi Kariyama**(Onomichi city university) 13:30-14:30Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)

**Keijyu Souno**(Math.-Sci., Tokyo Univ.) 15:00-16:00Moments of the derivatives of the Riemann zeta function (JAPANESE)

[ Abstract ]

In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

### 2012/04/03

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)

Moments of the derivatives of the Riemann zeta function (JAPANESE)

**Kazutoshi Kariyama**(Onomichi city university) 13:30-14:30Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)

**Keijyu Souno**(Math.-Sci., Tokyo Univ.) 15:00-16:00Moments of the derivatives of the Riemann zeta function (JAPANESE)

[ Abstract ]

In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.

### 2011/12/17

13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)

On the finite order Q-rational points on J_1 (N) (JAPANESE)

) 15:00-16:00

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)

**Masami Ohta**(Professor Emeritus of Tokai Univeristy) 13:30-14:30On the finite order Q-rational points on J_1 (N) (JAPANESE)

**Shushi Harashita**(Yokohama National University) 15:00-16:00

On the affineness of distinguished Deligne-Lusztig varieties (JAPANESE)