## Monthly Seminar on Arithmetic of Automorphic Forms

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

Seminar information archive

### 2014/10/11

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Takayuki Oda (Grad. School of Math.-Sci., Univ. of Tokyo) 13:30-14:30
The "secondary spherical function" of the discrete series representations of $SU(3,1)$ (following the memo of Tadashi Miyazaki) (JAPANESE)
Hideshi Takayanagi (Sakushin-Gakuin University) 15:00-16:00
Toward 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.)
Yoshihiro Onishi (Miejyo University) 13:30-14:30
Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)
Yoshihiro Onishi (Meijyo University) 15:00-16:00

### 2014/04/26

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Ryutarou Okazaki (Doushisha Univ. until March, 2014) 13:30-14:30
The 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) 15:00-16:00
Moduli 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.)
Yoshihiro Oonishi (Yamanashi Univ.) 13:30-14:30
Canceled for snow storm: Coble's hypersurface and defining equation of Kummer varieties (JAPANESE)
Atsuko Kogie (Toyama Univ.) 15:00-16:00
Generalization 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.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/02/01

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Bayarmagnai, G. (National University of Mongolia) 13:30-14:30
On 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.
Takayuki Oda (Univ. of Tokyo) 15:00-16:00
Minimal 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.

### 2014/01/11

14:00-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Dihua Jiang (School of Mathematics, University of Minnesota) 14:00-14:45
A 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) 15:00-15:45
A 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.)
Keijyu SOUNO (Tokyo University of Agriculture and Technology) 13:30-14:30
Pair 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.
Shigeki MATSUTANI

(Sagamihara city) 15:30-16:00
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.

### 2013/09/10

13:30-15:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Yuval Flicker (Ohio State Univ.) 13:30-15:00
Counting automorphic representations (JAPANESE)
Yuval Flicker (Ohio State University) 13:30-15:00
Counting automorphic representations II (Sept. 17) (JAPANESE)

### 2013/06/22

10:00-12:15   Room #123 (Graduate School of Math. Sci. Bldg.)
*** (***) 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.)
Kei-ichi Gunji (Chiba Inst. Tech) 10:00-11:00
On the computation of the ramified Siegel series associated with
trivial character (JAPANESE)
[ Abstract ]
Please check the Japanese version of the web page.
Masao Tsuzuki (Sophia University) 11:15-12:15
An 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.

### 2013/05/11

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Taku Ishii (Seikei Univeristy) 13:30-14:30
Symplectic-orthogonal theta lifts and explicit formulas for archimedean Whittaker functions (JAPANESE)
Takashi Ichikawa (Saga University) 15:00-16:00
Infinite 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.)
Miki Hirano (Ehime University) 13:30-14:30
Ramanujan circulant graphs and the Hardy-Littlewood conjecture (JAPANESE)
[ Abstract ]
TBA
Hiroaki Narita (Kumamoto University) 15:00-16:00
Generalized Whittaker functions on $G_{2}$ (JAPANESE)
[ Abstract ]
TBA

### 2012/09/15

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Tadashi Miyazaki (Kitazato University) 13:30-14:30
Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)
Hiro-aki Narita (Kumamoto University) 15:00-16:00
Strict 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.

### 2012/07/21

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
S. Takemori (Kyoto Univ., School of Science) 13:30-14:30
On 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}.

Noriko HIRATA-Kohno (Nihon University) 15:00-16:00
Polylogarithms 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.

### 2012/05/19

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Takashi Taniguchi (Kobe Univeristy) 13:30-14:30
TBA (JAPANESE)
Masao Tsuzuki (Sophia University) 15:00-16:00
TBA (JAPANESE)

### 2012/04/14

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Kazutoshi Kariyama (Onomichi city university) 13:30-14:30
Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)
Keijyu Souno (Math.-Sci., Tokyo Univ.) 15:00-16:00
Moments 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.

### 2012/04/03

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Kazutoshi Kariyama (Onomichi city university) 13:30-14:30
Explicit formula for the formal degree of the discrete series representations of GL_m(D). (JAPANESE)
Keijyu Souno (Math.-Sci., Tokyo Univ.) 15:00-16:00
Moments 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.

### 2011/12/17

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)
Masami Ohta (Professor Emeritus of Tokai Univeristy) 13:30-14:30
On 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)