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Takuya Yamauchi

Section

Graduate School of Science

Job title

Associate Professor

Degree

博士（理学）（広島大学）
修士（理学）（広島大学）

researchmap

https://researchmap.jp/7000019122

J-GLOBAL ID

201701004409612918

e-Rad No.

90432707

Education 4

Hiroshima University

- 2002
Hiroshima University　Graduate school of science　Mathematics

- 2002
Hiroshima University　Faculty of Science

- 2000
Hiroshima University　School of Science　Mathematics

- 2000

Committee Memberships 2

日本数学会　会員
Mathematical Society of Japan　Member

Professional Memberships 2

Mathematical Society of Japan
日本数学会

Research Interests 6

楕円曲線
Modular curves
elliptic curves
Automarphic forms
モジュラー曲線
保型形式

Research Areas 1

Natural sciences / Algebra /

Papers 16

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

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Algebra & Number Theory　18　(5)　993-1038　2024/04/16
Publisher: Mathematical Sciences Publishers
DOI： 10.2140/ant.2024.18.993 　

ISSN： 1937-0652

eISSN： 1944-7833
Distribution of Hecke eigenvalues for holomorphic Siegel modular forms

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Acta Arithmetica　215　(2)　161-177　2024
Publisher: Institute of Mathematics, Polish Academy of Sciences
DOI： 10.4064/aa230831-6-5 　

ISSN： 0065-1036

eISSN： 1730-6264
Equidistribution theorems for holomorphic Siegel modular forms for $$GSp_4$$; Hecke fields and n-level density

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Mathematische Zeitschrift　295　(3-4)　917-943　2020/08
Publisher: Springer Science and Business Media LLC
DOI： 10.1007/s00209-019-02378-7 　

ISSN： 0025-5874

eISSN： 1432-1823
An equidistribution theorem for holomorphic siegel modular forms for GSP4 and its applications

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

Journal of the Institute of Mathematics of Jussieu　19　(2)　351-419　2020/03/01
Publisher: Cambridge University Press
DOI： 10.1017/S147474801800004X 　

ISSN： 1475-3030 1474-7480
A uniform structure on subgroups of GL(n)(F-q) and its application to a conditional construction of Artin representations of GL(n) Peer-reviewed

Henry H. Kim, Takuya Yamauchi

JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY　32　(1)　75-99　2017/03

ISSN： 0970-1249

eISSN： 2320-3110
On some Siegel threefold related to the tangent cone of the Fermat quartic surface Peer-reviewed

Takeo Okazaki, Takuya Yamauchi

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS　21　(3)　585-630　2017

ISSN： 1095-0761

eISSN： 1095-0753
Cusp forms on the exceptional group of type E-7 Peer-reviewed

Henry H. Kim, Takuya Yamauchi

COMPOSITIO MATHEMATICA　152　(2)　223-254　2016/02

DOI： 10.1112/S0010437X15007538 　

ISSN： 0010-437X

eISSN： 1570-5846
On Intermediate Jacobians of Cubic Threefolds Admitting an Automorphism of Order Five Peer-reviewed

Bert van Geemen, Takuya Yamauchi

PURE AND APPLIED MATHEMATICS QUARTERLY　12　(1)　141-164　2016

ISSN： 1558-8599

eISSN： 1558-8602
A conditional construction of Artin representations for real analytic Siegel cusp forms of weight (2,1) Peer-reviewed

Henry H. Kim, Takuya Yamauchi

ADVANCES IN THE THEORY OF AUTOMORPHIC FORMS AND THEIR L-FUNCTIONS　664　225-260　2016

DOI： 10.1090/conm/664/13061 　

ISSN： 0271-4132
On the class numbers of the fields of the p(n)-torsion points of certain elliptic curves over Q Peer-reviewed

Fumio Sairaiji, Takuya Yamauchi

JOURNAL OF NUMBER THEORY　156　277-289　2015/11

DOI： 10.1016/j.jnt.2015.04.004 　

ISSN： 0022-314X

eISSN： 1096-1658
On the rational K-2 of a curve of GL(2) type over a global field of positive characteristic Peer-reviewed

Masataka Chida, Satoshi Kondo, Takuya Yamauchi

JOURNAL OF K-THEORY　14　(2)　313-342　2014/10

DOI： 10.1017/is014006024jkt272 　

ISSN： 1865-2433

eISSN： 1865-5394
The Rank of Jacobian Varieties over the Maximal Abelian Extensions of Number Fields: Towards the Frey-Jarden Conjecture Peer-reviewed

Fumio Sairaiji, Takuya Yamauchi

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES　55　(4)　842-849　2012/12

DOI： 10.4153/CMB-2011-140-5 　

ISSN： 0008-4395
A generalization of Sen-Brinon's theory Peer-reviewed

Takuya Yamauchi

MANUSCRIPTA MATHEMATICA　133　(3-4)　327-346　2010/11

DOI： 10.1007/s00229-010-0372-2 　

ISSN： 0025-2611
On curves with split Jacobians Peer-reviewed

Takuya Yamauchi

COMMUNICATIONS IN ALGEBRA　36　(4)　1419-1425　2008/04

DOI： 10.1080/00927870701866622 　

ISSN： 0092-7872
THE MODULARITY OF Q-CURVES OF DEGREE 43 Peer-reviewed

Takuya Yamauchi

HOUSTON JOURNAL OF MATHEMATICS　34　(4)　1025-1035　2008

ISSN： 0362-1588
An observation on the cyclicity of the group of the F-p-rational points of abelian surfaces Peer-reviewed

Takuya Yamauchi

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS　24　(3)　307-318　2007/10

ISSN： 0916-7005

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Research Projects 17

New developments of automorphy of Galois representations and Serre conjecture.

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2019/04/01 - 2024/03/31
Study of arithmetic gometry by p-adic methods

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

Institution: Tohoku University

2018/04/01 - 2023/03/31
A experimental study of arithmetic local systems with geometric origins and unsolved problems in arithmetic geometry

TSUZUKI Nobuo, Yamauchi Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2015/04/01 - 2019/03/31

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While there are lots of unsolved problems in arithmetic geometry, it is difficult to construct explicit examples because of abstraction. Using the arithmetic family of higher dimensional Calabi-Yau varieties, which has been constructed by the author, over the projective line of invertible 2, (1) we show an irreducible component of the degenerated fiber is a rigid Calabi-Yau variety over the field of rational numbers, and prove the modularity and the algebraicity of cohomology classes, and (2) study a 2-adic model and construct a K3 surface over a real quadratic field with everywhere good reduction. We also study p-adic properties of Frobenius actions arithmetically, and prove the constancy of Newton polygons of arbitrary F-isocrystals on Abelian varieties. This result has not been known so far.
The geometry of Shimura varieties over positive characteristic and the development of Galois representations

Yamauchi Takuya, Chida Masataka, Miyauchi Michitaka

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (C)

2015/04/01 - 2019/03/31

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The study conducted during the project was analysis of Serre weight. The Serre weight is a concept necessary to formulate modularity problem of the residual Galois representation, and specifies the possibility of the weights of the corresponding automorphic forms. In this research, we introduce the theta operators as one of the tools to analyze the Serre weight, and when the algebraic group is GSp4, we succeeded in giving a concrete expression of the theta operators. We use the modular lifting theorems to prove the Serre weight theorem in a fairly general case for GSp4 over totally real fields, and further a list of the possible Serre weight of corresponding automorphic forms was described completely in terms of the local properties of a given mod p Galois representation.
New developments in number theoretic geometry, topology, and algorithm

Matsumoto Makoto, TAMAGAWA AKIO, Mochizuki Shinichi, Hoshi Yuichiro, Tsuzuki Nobuo, Terasoma Tomohide, Saito Shuji, Tsuji Takeshi, Shiho Atsushi, Morita Shigeyuki, Shimada Ichiro, Kimura Shun-ichi, Kamada Seiichi, Sakuma Makoto, Ishii Akira, Takahashi Nobuyoshi, Hiranouchi Toshiro, Haramoto Hiroshi, Kaneko Masanobu, Taguchi Yuichiro, Furusho Hidekazu, Nishimura Takuji, Hagita Mariko, Yamauchi Takuya, Asakura Masanori, Mizusawa Yasushi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

2011/04/01 - 2016/03/31

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We studied pure mathematics such as number theory, algebra, geometry, in an interdisciplinary manner. In addition, we studied there application in other branch of science and engineering. In pure mathematics side, we constructed a mixed elliptic motif obtained from universal family of elliptic curves. Also, given an l-adic linear representation of arithmetic fundamental group of an algebraic curve, we compared the image of the representation and the image of the Galois group of k-rational point of curves. As for applicational research, we developped a fast numerical integration algorithm based on quasi-Monte Carlo. The method depends on a point set (called Niederreiter-Xing point sets) whose basis is in the theory of rational points of algebraic curves). We introduced a new criteria for uniformity of point set named WAFOM, and our algorithm uses point sets obtained by scrambling Niederreiter-Xing point sets whose WAFOM value is small. Its effectiveness is empirically confirmed.
Automorphic forms, algebraic varieties and Iwasawa theory

OKAZAKI Takeo, YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

Institution: Nara Women's University

2012/04/01 - 2015/03/31

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We established functional equations for automorphic representations of GU(2,2), and a New form theory corresponding to them. We call D-paramodular subgroups which fix the new forms. In particular, when the automorphic representation is distinguished, it has a D-paramodular Shalika period. By considering the theta correspondence between GSp(4) and GU(2,2), we give a proof for a conjecture of van Geemen and van Straten.
Integral structures of arithmetic differential equations and geometries behind them

TSUZUKI Nobuo, YAMAUCHI Takuya, TAKAHASHI Nobuyoshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2012/04/01 - 2015/03/31

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We studied properties of the arithemtic family of Calabi-Yau varieties, constructed by the representative of this research, for which the period integral is a generalized hypergeometric functions. In particular, if the dimension is odd, we found a semistable family around a degenerated fiber such that the number of irreducible components of the special fiber is two among which the one is rational and the other has an interesting natures with respect to arithmetic geometry. In particuler, we proved the modularity of the special fiber in dimension 3. In the case of dimension 2, we constructed a semistable family over an extension of Z which is ramified only at 2 and got a K3 surface over an algebraic number field such that it has a good reduction everywhere.
The study of Galois deformations and an inductive structure of their automorphy

YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

Institution: Kagoshima University

2011/04/28 - 2015/03/31

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In this research project, the researcher carried out the program to study a correspondence between Galois representations (in the algebraic side) and automorphic forms (in the analytic side). Usually we understand it via p-adic Galois representations and it's reduction which is often called mod p representation. Then we have to divide the modularity problem into the type of mod p representation in question and plug them into the full modularity problem. In this project He studied the property of modular mod p representation so that any such representation could be reduced to a manageable class of mod p representation.
A study of arithemetic geometry by p-aidc methods

TSUZUKI NOBUO, KATO Fumiharu, SHIHO Atsushi, YAMAZAKI Takao, NAKAJIMA Yukiyoshi, YAMAUCHI Takuya, KAWAMURA Hisa-aki, ABE Tomoyuki, SUWA Noriyuki

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

Institution: Tohoku University

2010/04/01 - 2014/03/31

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We investigated the foundation of p-adic methods in arithmetic geometry, rigid analytic technique and cohomology theory arising from differential forms (i.e., p-adic cohomology), and applied them to study arithmetic varieties. We construct p-adic Clemens-Schmid exact sequence for semistable families over algebraic curves of positive characteristic, which is a p-adic analogue of exact sequence describing kernel and cokernel of monodromy operations for semistable families over the complex unit disk. We studied the purity theorem for isocrystals and established the full faithfulness of restriction functors to open subschemes for isocrystals on geometrically unibranch varieties of positive characteristic. As a consequence, we proved pure of weight 1 for first rigid cohomology of proper and geometrically unibranch varieties. We also developed the weight theory in p-adic cohomology and the theory of arithmetic D-modules.
A local and global study of arithmetic varieties determined by arithmetic differential equations

TSUZUKI Nobuo, YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Challenging Exploratory Research

Institution: Tohoku University

2009 - 2011

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We constructed an arithmetic family of Calabi-Yau varieties on the projective line whose period integral is a generalized hypergeometric function, and determined the relative cohomology of Betti, de Rham, etale and crystalline realizations. This family is a higher dimensional version of Legenedre's family of elliptic curves. The family of Calabi-Yau is obtained by a desingularization which is given explicitly, and has a semistable degeneration at 0. The cohomologies can be calculated by applying weight spectral sequences. Moreover, we have a result on modularity for rational fibers.
Research on explicit constructions of motives associated to automorphic forms

YAMAUCHI Takuya

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Young Scientists (B)

2007 - 2010

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(1) A construction of Siegel paramodular form corresponding to some rigid Calabi-Yau threefold. (2) A construction of endoscopic lifts associated to some Siegel modular variety and a computation of L-function of that variety. (3) A construction of a Calabi-Yau family having continuous Hodge number over the projective line minus three points and potential automorphy of each fiber. For (3), we explain more concretely. From local systems of rank one over the open curve U : projective line minus three points, by using convolution we construct hypergeometric sheaves F_n/U of rank n+1, weight n for each natural number n and then we construct a Calabi-Yau family whose middle cohomology sheave realizes F_n up to algebraic cycles when n is even. As an application, we prove potential automorphy of each fiber.
New developments in number theory and geometry : arithmetic topology, categorical arithmetic geometry, algorithm

MATSUMOTO Makoto, TAMAGAWA Akio, MOCHIZUKI Shinichi, TSUZUKI Nobuo, KIMURA Shunichi, TERASOMA Tomohide, MORITA Shigeyuki, HIROSE Susumu, MORITA Takehiko, YOSHINO Masafumi, NAGAI Yoshitaka, SUGAWA Toshiyuki, TAKAHASHI Nobuyoshi, KANEKO Masanobu, TAGUCHI Yuichirou, ITO Hiroyuki, NISHIMURA Takuji, SAITO Shuji, TSUJI Takeshi, MORITA Yoshiyuki, SHIMADA Ichirou, ISHII Akira, YAMAUCHI Takuya, SHIHO Atsushi, SAITO Mutsuo, HARAMOTO Hiroshi

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (A)

Institution: Hiroshima University

2007 - 2010

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By using methods of geometric topology in arithmetic geometry, knowledges on topology (such as the cohomology of the mapping class groups) are utilized in researches on arithmetic geometry (such as outer Galois representations).(2)We developped a frame work to detect objects in arithmetic geometry by means of its combinatorial and categorical data.(3)We developped algebraic and geometric alogrithm for applications such as evaluation of pseudorandom number generators.
A study of arithmetic varieties by p-adic methods

TSUZUKI Nobuo, KATO Fumiharu, SHIHO Atsushi, NAKAJIMA Yoshiyuki, MATSUDA Shigeki, ITO Hiroyuki, KIMURA Shunichi, TAGUCHI Yuichiro

Offer Organization: Japan Society for the Promotion of Science

System: Grants-in-Aid for Scientific Research

Category: Grant-in-Aid for Scientific Research (B)

2005 - 2008
代数曲線のヤコビ多様体の分解に関する研究 Competitive

2004 - 2006
A Research on the decomposition of Jacobian varieties Competitive

2002 - 2006
On decomposition of Jacobian Varieties Competitive

2002 - 2004
ヤコビ多様体の分解について Competitive

2002 - 2004

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