Taku Ishii

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20112024

most citedWhittaker functions on orthogonal groups of odd degree

4 citations · 6 across the 5 of their papers we have counts for

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math.NT2024

Whittaker functions on GL(4,R) and archimedean Bump--Friedberg integrals

Miki Hirano, Taku Ishii, Tadashi Miyazaki

We give explicit formulas of Whittaker functions on GL(4,R) for all irreducible generic representations. As an application, we determine test vectors which attain the associated L-…

math.NT2021★ 1 cited

Archimedean zeta integrals for $G L (3) \times G L (2)$

Miki Hirano, Taku Ishii, Tadashi Miyazaki

In this article, we give explicit formulas of archimedean Whittaker functions on $G L (3)$ and $G L (2)$ . Moreover, we apply those to the calculation of archimedean zeta integrals for…

math.NT2020

Calculus of archimedean Rankin--Selberg integrals with recurrence relations

Taku Ishii, Tadashi Miyazaki

Let $n$ and $n^{'}$ be positive integers such that $n - n^{'} \in {0, 1}$ . Let $F$ be either $R$ or $C$ . Let $K_{n}$ and $K_{n^{'}}$ be maximal compact subgroups of $\mathrm{G…

math.NT2011★ 4 cited

Whittaker functions on orthogonal groups of odd degree

Taku Ishii

We give explicit formulas for Whittaker functions for the class one principal series representations of the orthogonal groups $S O_{2 n + 1} (R)$ of odd degree. Our formulas are simi…

math.NT2011★ 1 cited

Archimedean zeta integrals on $G L_{n} \times G L_{m}$ and $S O_{2 n + 1} \times G L_{m}$

Taku Ishii, Eric Stade

In this paper, we evaluate archimedean zeta integrals for automorphic $L$ -functions on $G L_{n} \times G L_{n - 1 + ℓ}$ and on $S O_{2 n + 1} \times G L_{n + ℓ}$ , for $ℓ = - 1$ , $0$ , and $…