Monthly Seminar on Arithmetic of Automorphic Forms

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

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.