Takuya Yamauchi

activity

20102026

most citedCusp forms for exceptional group of type

E_{7}

12 citations · 55 across the 36 of their papers we have counts for

collaborators

39 papers

math.NT2026

Isogeny graphs associated to Moret-Bailly families of supersingular abelian surfaces

Toshiyuki Katsura, Takuya Yamauchi

For an odd prime $p$ and any prime $ℓ \neq = p$ , we study finite directed graphs arising from the set of all equivalence classes of Moret-Bailly families of abelian surfaces in cha…

math.NT2025

Regulators on some abelian coverings of $P^{1}$ minus $n + 2$ points

Yusuke Nemoto, Takuya Yamauchi

In this paper, we construct certain rational or integral elements in the motivic cohomology of superelliptic curves which are quotient curves of abelian coverings of $P^{1}$ …

math.NT2025

The $L$ -function of the surface parametrizing cuboids

Madoka Horie, Takuya Yamauchi

In this note, we compute the $L$ -function of the projective smooth surface $S$ over $Q$ that parametrizes cuboids whose geometric properties are studied in detail by Stoll…

math.NT2025

The non-existence of some Galois representations of moderate dimension in small characteristic

Alexandru Ghitza, Takuya Yamauchi

Refining arguments of Hyunsuk Moon, under the assumption of the Generalized Riemann Hypothesis, we prove the non-existence of irreducible mod 2 Galois representations unramified ou…

math.NT2025

The residual monodromy for the Dwork family in even characteristic and its applications to Galois representations

Takuya Yamauchi

We study the residual monodromy representations associated to the Dwork family in characteristic two. Various applications involving 2-adic and mod 2 Galois representations are dis…

math.NT2023

Harder's conjecture II

Hiraku Atobe, Masataka Chida, Tomoyoshi Ibukiyama +2

Let $f$ be a primitive form of weight $2 k + j - 2$ for $S L_{2} (Z)$ , and let $P$ be a prime ideal of the Hecke field of $f$ . We denote by $S p_{m} (Z)$ the Siegel modular group of degree $m$ .…

math.NT2022

A new theta cycle for $GS p_{4}$ and an Edixhoven type theorem

Takuya Yamauchi

In this paper, we investigate a new theta cycle for $GS p_{4} / Q$ by using author's theta operators defined in the previous work. In the course of the construction, we also mo…

math.NT2022

Isogeny graphs on superspecial abelian varieties: Eigenvalues and Connection to Bruhat-Tits buildings

Yusuke Aikawa, Ryokichi Tanaka, Takuya Yamauchi

We study for each fixed integer $g \geq 2$ , for all primes $ℓ$ and $p$ with $ℓ \neq = p$ , finite regular directed graphs associated with the set of equivalence classes of $ℓ$ …

math.NT2021

Harder's conjecture I

Hiraku Atobe, Masataka Chida, Tomoyoshi Ibukiyama +2

Let $f$ be a primitive form with respect to $S L_{2} (Z)$ . Then we propose a conjecture on the congruence between the Klingen-Eisenstein lift of the Duke-Imamoglu-Ikeda lift of $f$ and…

math.NT2021★ 1 cited

A remark on conductor, depth and principal congruence subgroups

Michitaka Miyauchi, Takuya Yamauchi

In this paper we study a relation between conductor, depth, and the level of principal congruence subgroups for irreducible admissible representations of $GL_{n} (F)$ for a non-…

math.AG2021

On finiteness theorems for automorphic forms

Takuya Yamauchi

In this paper, for any Shimura datum $(G, D)$ satisfying reasonable conditions so that many interesting cases satisfy, we prove some finiteness theorems for any graded vec…

math.NT2021★ 2 cited

Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

We prove equidistribution theorems for a family of holomorphic Siegel cusp forms of general degree in the level aspect. Our main contribution is to estimate unipotent contributions…

math.NT2021★ 2 cited

Transfers of some Hecke elements for possibly ramified base change in GL_n

Takuya Yamauchi

In this paper we prove an explicit matching theorem for some Hecke elements in the case of (possibly ramified) cyclic base change for general linear groups over local fields of cha…

math.NT2020

Period of the Ikeda type lift for $E_{7, 3}$

Hidenori Katsurada, Henry H. Kim, Takuya Yamauchi

In our previous work, he second and the third named authors constructed the Ikeda type lift for the exceptional group $E_{7, 3}$ from an elliptic modular cusp form. In this paper, w…

math.NT2020

Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields

Alexandru Ghitza, Takuya Yamauchi

Let $C$ be a genus two hyperelliptic curve over a totally real field $F$ . We show that the mod 2 Galois representation $\barρ_{C,2}\colon\mathrm{Gal}(\bar{F}/F)\to \mathrm{GSp}_4(\…

math.NT2020

Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials

Nobuo Tsuzuki, Takuya Yamauchi

In this paper, we determine mod $2$ Galois representations $ρ ˉ_{ψ, 2} : G_{K} := Gal (K ˉ / K) ⟶ GSp_{4} (F_{2})$ associated to the mirror motives of rank…

math.NT2020★ 2 cited

Serre weights for $GS p_{4}$ over totally real fields

Takuya Yamauchi

We prove the existence of a potentially diagonalizable lift of a given automorphic mod $p$ Galois representation $\overlineρ:{\rm Gal}(\overline{F}/F)\longrightarrow {\rm GSp}_4(\o…

math.NT2019

Congruences of Siegel Eisenstein series of degree two

Takuya Yamauchi

In this paper we study congruences between Siegel Eisenstein series and Siegel cusp forms for Sp_4(Z).

math.NT2018

Non-vanishing of Miyawaki type lift

Henry H. Kim, Takuya Yamauchi

Miyawaki type lifts are kinds of Langlands functorial lifts and a special case was first conjectured by Miyawaki and proved by Ikeda for Siegel cusp forms. Since then, such a lift…

math.NT2018★ 5 cited

A reformulation of the Siegel series and intersection numbers

Sungmun Cho, Takuya Yamauchi

In this paper, we will explain a conceptual reformulation and inductive formula of the Siegel series. Using this, we will explain that both sides of the local intersection multipli…

math.NT2018★ 1 cited

Equidistribution theorems for holomorphic Siegel modular forms for $GS p_{4}$ ; Hecke fields and $n$ -level density

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

This paper is a continuation of the author's previous wotk. We supplement four results on a family of holomorphic Siegel cusp forms for $GS p_{4} / Q$ . First, we improve the re…

math.NT2018

Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences

Sungmun Cho, Shunsuke Yamana, Takuya Yamauchi

We give a formula for certain values and derivatives of Siegel series and use them to compute Fourier coefficients of derivatives of the Siegel Eisenstein series of weight g/2 and…

math.NT2017★ 1 cited

Higher level cusp forms on the exceptional group of type $E_{7}$

Henry H. Kim, Takuya Yamauchi

By using new techniques with the degenerate Whittaker functions found by Ikeda-Yamana, we construct higher level cusp form on $E_{7, 3}$ , called Ikeda type lift, from any Hecke cusp…

math.NT2017★ 1 cited

An explicit formula for the extended Gross-Keating datum of a quadratic form

Sungmun Cho, Tamotsu Ikeda, Hidenori Katsurada +2

In this paper, we give a formula for the extended Gross-Keating datum of a quadratic form defined over a finite extension of $Z_{p}$ (for $p > 2$ ) or a finite unramified exten…

Isogeny graphs associated to Moret-Bailly families of supersingular abelian surfaces

Regulators on some abelian coverings of P1 minus n+2 points

The L-function of the surface parametrizing cuboids

The non-existence of some Galois representations of moderate dimension in small characteristic

The residual monodromy for the Dwork family in even characteristic and its applications to Galois representations

Harder's conjecture II

A new theta cycle for GSp4​ and an Edixhoven type theorem

Isogeny graphs on superspecial abelian varieties: Eigenvalues and Connection to Bruhat-Tits buildings

Harder's conjecture I

A remark on conductor, depth and principal congruence subgroups

On finiteness theorems for automorphic forms

Equidistribution theorems for holomorphic Siegel cusp forms of general degree: the level aspect

Transfers of some Hecke elements for possibly ramified base change in GL_n

Period of the Ikeda type lift for E7,3​

Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields

Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials

Serre weights for GSp4​ over totally real fields

Congruences of Siegel Eisenstein series of degree two

Non-vanishing of Miyawaki type lift

A reformulation of the Siegel series and intersection numbers

Equidistribution theorems for holomorphic Siegel modular forms for GSp4​; Hecke fields and n-level density

Derivatives of Eisenstein series of weight 2 and intersections of modular correspondences

Higher level cusp forms on the exceptional group of type E7​

An explicit formula for the extended Gross-Keating datum of a quadratic form

Regulators on some abelian coverings of $P^{1}$ minus $n + 2$ points

The $L$ -function of the surface parametrizing cuboids

A new theta cycle for $GS p_{4}$ and an Edixhoven type theorem

Period of the Ikeda type lift for $E_{7, 3}$

Serre weights for $GS p_{4}$ over totally real fields

Equidistribution theorems for holomorphic Siegel modular forms for $GS p_{4}$ ; Hecke fields and $n$ -level density

Higher level cusp forms on the exceptional group of type $E_{7}$