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2016 Fiscal Year Final Research Report

On special values of automorphic L-functions

Research Project

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Project/Area Number 25400020
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionOsaka City University

Principal Investigator

FURUSAWA Masaaki  大阪市立大学, 大学院理学研究科, 教授 (50294525)

Project Period (FY) 2013-04-01 – 2017-03-31
Keywords保型L函数 / L函数の特殊値 / テータ対応
Outline of Final Research Achievements

In a joint work with Kazuki Morimoto of Kobe University, we proved one direction of the Gross-Prasad conjecture in the case of special Bessel periods for SO(2n+1). Namely we proved that the non-vanishing of the special Bessel period for SO(2n+1) implies the non-vanishing of the central value of the corresponding L-function. We also proved the converse in some cases.
In another joint work with Kazuki Morimoto, we proved the algebraicity of some critical values of the tensor product L-functions for SO(V) times GL(2) where V is anisotropic. Our result involves some unbalanced cases of the Rankin triple L-function for GL(2).

Free Research Field

保型L函数

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Published: 2018-03-22  

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