Faculty of International Social Sciences

山田 一紀

ヤマダ カズキ  (Kazuki Yamada)

基本情報

所属
学習院大学 理学部 数学科 助教
学位
博士(理学)(2020年3月 慶應義塾大学)

研究者番号
20896683
J-GLOBAL ID
201401090887066393
researchmap会員ID
B000241714

論文

 6
  • Kenichi Bannai, Hohto Bekki, Kei Hagihara, Tatsuya Ohshita, Kazuki Yamada, Shuji Yamamoto
    Advances in Mathematics 448 Paper No. 109716 2024年6月  査読有り
  • Kenichi Bannai, Kei Hagihara, Kazuki Yamada, Shuji Yamamoto
    Transactions of the American Mathematical Society, Series B 10(19) 613-635 2023年5月2日  
    <p>It is known that the special values at nonpositive integers of a Dirichlet -function may be expressed using the generalized Bernoulli numbers, which are defined by a generating function. The purpose of this article is to consider the generalization of this classical result to the case of Hecke -functions of totally real fields. Hecke -functions may be expressed canonically as a finite sum of zeta functions of Lerch type. By combining the non-canonical multivariable generating functions constructed by Shintani [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), pp. 393–417], we newly construct a canonical class, which we call the Shintani generating class, in the equivariant cohomology of an algebraic torus associated to the totally real field. Our main result states that the specializations at torsion points of the derivatives of the Shintani generating class give values at nonpositive integers of the zeta functions of Lerch type. This result gives the insight that the correct framework in the higher dimensional case is to consider higher equivariant cohomology classes instead of functions.</p>
  • Kenichi Bannai, Kei Hagihara, Kazuki Yamada, Shuji Yamamoto
    Journal für die reine und angewandte Mathematik (Crelles Journal) 2022(791) 53-87 2022年10月1日  査読有り
    Abstract The purpose of this article is to newly define the p-adic polylogarithmas an equivariant class in the cohomology of a certain infinite disjoint union of algebraic toriassociated to a totally real field.We will then express the special values of p-adic L-functions interpolatingnonpositive values of Hecke L-functions of the totally real field in terms ofspecial values of these p-adic polylogarithms.
  • Veronika Ertl, 山田 一紀
    Rendiconti del Seminario Matematico della Universita di Padova 145 213-291 2021年5月  査読有り
    掲載決定済
  • 坂内健一, 萩原啓, 山田一紀, 山本修司
    Mathematische Zeitschrift 296(3-4) 1787-1817 2020年12月  査読有り

MISC

 3

講演・口頭発表等

 27

教育業績(担当経験のある科目)

 9

所属学協会

 1

共同研究・競争的資金等の研究課題

 3