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Kenichi Namikawa

Publications and source records attributed to Kenichi Namikawa.

7 recordsLinked to original sources
arXiv2024

Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$

After introducing the notion of uniform integrality of critical values of the Rankin-Selberg $L$-functions for $\mathrm{GL}_{n}\times \mathrm{GL}_{n-1}$, we study it when the base field is totally imaginary. For this purpose, we adopt specific models of highest weight representations of the general linear groups, construct the Eichler-Shimura classes for $\mathrm{GL}_{n}$ and $\mathrm{GL}_{n-1}$ in an explicit manner, and then evaluate the cohomological cup product of them, by making the best use of Gel'fand-Tsetlin basis.

math.NT↗
arXiv2022

A motivic interpretation of Whittaker periods for $\mathrm{GL}_n$

Admitting the existence of conjectural motives attached to cohomological irreducible cuspidal automorphic representations of $\mathrm{GL}_n$, we write down Raghuram and Shahidi's Whittaker periods in terms of Yoshida's fundamental periods when the base field is a totally real number field or a CM field.

math.NT↗
arXiv2020

A cohomological interpretation of archimedean zeta integrals for ${\rm GL}_3\times {\rm GL}_2$

By studying an explicit form of the Eichler--Shimura map for ${\rm GL}_3$, we describe a precise relation between critical values of the complete $L$-function for the Rankin--Selberg convolution ${\rm GL}_3 \times {\rm GL}_2$ and the cohomological cup product of certain rational cohomology classes which are uniquely determined up to rational scalar multiples from the cuspidal automorphic representations under consideration. This refines rationality results on critical values due to Raghuram et al.

math.NT↗
arXiv2019

A construction of $p$-adic Asai $L$-functions for ${\rm GL}_2$ over CM fields

We give a construction of $p$-adic Asai $L$-functions for cohomological cuspidal automorphic representations of ${\rm GL}_2$ over CM fields. If the base field is imaginary quadratic, Loeffler-Williams recently constructed the $p$-adic Asai $L$-functions. We generalize their construction to the case that the base fields are general CM fields.

math.NT↗
arXiv2018

Explicit inner product formulas and Bessel period formulas for HST lifts

We explicitly give an inner product formula and a Bessel period formula for theta series on GSp(4), which was studied by Harris, Soudry and Taylor. As a consequence, we prove a non-vanishing of the theta series of small weights and we give a criterion for the non-vanishing of the theta series modulo a prime.

math.NT↗
arXiv2016

Bessel periods and the non-vanishing of Yoshida lifts modulo a prime

We give an explicit construction of vector-valued Yoshida lifts and derive a formula of the Bessel periods of Yoshida lifts, by which we prove the non-vanishing modulo a prime of Yoshida lifts attached to a pair of elliptic modular newforms. As a consequence, we obtain a new proof of the non-vanishing of Yoshida lifts.

math.NT↗