Henry H. Kim

activity

19992022

most citedSymmetric cube L-functions for GL_2 are entire

39 citations · 87 across the 19 of their papers we have counts for

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20 papers · 1 filter

math.NT2022

Twisted Koecher-Maass series of the Ikeda type lift for the exceptional group of type $E_{7, 3}$

Hidenori Katsurada, Henry H. Kim

We compute the twisted Koecher-Maass series of the first and second kind of the Ikeda type lift for the exceptional group of type $E_{7, 3}$ . As an application, we obtain their rati…

math.NT2022

Rankin-Selberg convolution for the Duke-Imamoglu-Ikeda lift

Hidenori Katsurada, Henry H. Kim

For two Hecke eigenforms $h_{1}$ and $h_{2}$ in the Kohnen plus space of half-integral weight, let $I_{n} (h_{1})$ and $I_{n} (h_{2})$ be the Duke-Imamoglu-Ikeda lift of $h_{1}$ and $h_{2}$ , respect…

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.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.NT2019★ 1 cited

The Shintani double zeta functions

Henry H. Kim, Masao Tsuzuki, Satoshi Wakatsuki

In this paper, we give an explicit formula of the Shintani double zeta functions with any ramification in the most general setting of adeles over an arbitrary number field. Three a…

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★ 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.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.NT2016★ 5 cited

An equidistribution theorem for holomorphic Siegel modular forms for $GS p_{4}$

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for $GS p_{4} / Q$ in various aspects. A main tool is Arthur's invariant trace formula. While…

math.NT2016★ 7 cited

Extreme residues of Dedekind zeta functions

Peter J. Cho, Henry H. Kim

In a family of $S_{d + 1}$ -fields ( $d = 2, 3, 4$ ), we obtain the true upper and lower bound of the residues of Dedekind zeta functions except for a density zero set. For $S_{5}$ -fields, we…

math.NT2016

The average of the smallest prime in a conjugacy class

Peter J. Cho, Henry H. Kim

Let $C$ be a conjugacy class of $S_{n}$ and $K$ an $S_{n}$ -field. Let $n_{K, C}$ be the smallest prime which is ramified or whose Frobenius automorphism Frob $_{p}$ does not belong to $C$ .…

math.NT2015

Miyawaki type lift for $GS p in (2, 10)$

Henry H. Kim, Takuya Yamauchi

Let $T_{2}$ (resp. $T$ ) be the Hermitian symmetric domain of $S p in (2, 10)$ (resp. $E_{7, 3}$ ). In the previous work, we constructed holomorphic cusp forms on $\mathfra…

math.NT2015

Ikeda type construction of cusp forms

Henry H. Kim, Takuya Yamauchi

This is a survey of results on the construction of holomorphic cusp forms on tube domains originally initiated by Ikeda. Besides a survey it includes conjectures and possible appli…

math.NT2015

Central limit theorem for Artin $L$ -functions

Peter J. Cho, Henry H. Kim

We show that the sum of the traces of Frobenius elements of Artin $L$ -functions in a family of $G$ -fields satisfies the Gaussian distribution under certain counting conjectures. We…

math.NT2014★ 12 cited

Cusp forms for exceptional group of type $E_{7}$

Henry H. Kim, Takuya Yamauchi

Let $G$ be the connected reductive group of type $E_{7, 3}$ over $Q$ and $T$ be the corresponding symmetric domain in $C^{27}$ . Let $Γ=\bf{G}(\math…

math.NT2014

Artin representations for $G L_{n}$

Henry H. Kim, Takuya Yamauchi

Let $π$ be a cuspidal automorphic representation of $G L_{n} (A_{Q})$ which satisfies certain reasonable assumptions such as integrality of Hecke polynomials, the exist…

math.NT2013★ 1 cited

Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras

Henry H. Kim, Kyu-Hwan Lee, Yichao Zhang

In this paper, we compute basis elements of certain spaces of weight 0 weakly holomorphic modular forms and consider the integrality of Fourier coefficients of the modular forms. W…

math.NT2013

Artin representations for GSp_4 attached to real analytic Siegel cusp forms of weight (2,1)

Henry H. Kim, Takuya Yamauchi

Let $F$ be a vector-valued real analytic Siegel cusp eigenform of weight $(2, 1)$ with the eigenvalues $- \frac{5}{12}$ and 0 for the two generators of the center of the algebra consi…

math.NT2004★ 15 cited

Functorial products for $G L_{2} \times G L_{3}$ and the symmetric cube for $G L_{2}$

Henry H. Kim, Freydoon Shahidi, Colin J. Bushnell +1

In this paper we prove two new cases of Langlands functoriality. The first is a functorial product for cusp forms on $G L_{2} \times G L_{3}$ as automorphic forms on $G L_{6}$ , from which we…

math.NT1999★ 39 cited

Symmetric cube L-functions for GL_2 are entire

Henry H. Kim, Freydoon Shahidi

The purpose of this paper is to prove the long awaited holomorphy of the third symmetric power L-functions attached to nonmonomial cusp forms of GL_2 over an arbitrary number field…

Twisted Koecher-Maass series of the Ikeda type lift for the exceptional group of type E7,3​

Rankin-Selberg convolution for the Duke-Imamoglu-Ikeda lift

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

Period of the Ikeda type lift for E7,3​

The Shintani double zeta functions

Non-vanishing of Miyawaki type lift

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

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

An equidistribution theorem for holomorphic Siegel modular forms for GSp4​

Extreme residues of Dedekind zeta functions

The average of the smallest prime in a conjugacy class

Miyawaki type lift for GSpin(2,10)

Ikeda type construction of cusp forms

Central limit theorem for Artin L-functions

Cusp forms for exceptional group of type E7​

Artin representations for GLn​

Weakly holomorphic modular forms and rank two hyperbolic Kac-Moody algebras

Artin representations for GSp_4 attached to real analytic Siegel cusp forms of weight (2,1)

Functorial products for GL2​×GL3​ and the symmetric cube for GL2​

Symmetric cube L-functions for GL_2 are entire

Twisted Koecher-Maass series of the Ikeda type lift for the exceptional group of type $E_{7, 3}$

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

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 $E_{7}$

An equidistribution theorem for holomorphic Siegel modular forms for $GS p_{4}$

Miyawaki type lift for $GS p in (2, 10)$

Central limit theorem for Artin $L$ -functions

Cusp forms for exceptional group of type $E_{7}$

Artin representations for $G L_{n}$

Functorial products for $G L_{2} \times G L_{3}$ and the symmetric cube for $G L_{2}$