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Various types of multiple polylogarithms and related zeta values (Analytic Number Theory and Related Topics)

open access: yesVarious types of multiple polylogarithms and related zeta values (Analytic Number Theory and Related Topics)
この論説では,既に出版されている[10,11]に含まれているレベル4の多重L値や2変数の多重ポリログに関する結果を含むような,より一般的な枠組みにおける結果を紹介する.具体的には,既存のものとは異なる多重ポリログを,[1]で考察されている手法がうまく働くような形で定義し,多重ゼータ値の一般化にあたる概念を定義することで,それらの値の間の関係式を与える.具体例として,多重L値や多重ポリログの既知の関係式に加えて,これまでに知られていないような多重級数の値の間の関係式も与えることができる.これらの詳細や証明については,現在準備中の[12]を参照いただきたい.
Masanobu Kaneko, Hirofumi Tsumura
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A generalized uniformly bounded multiplicity theorem (Developments in Representation Theory and Related Topics)

open access: yesA generalized uniformly bounded multiplicity theorem (Developments in Representation Theory and Related Topics)
Let P be a minimal parabolic subgroup of a real reductive Lie group G and H a closed subgroup of G. Then it is proved by T. Kobayashi and T. Oshima that the regular representation C∞ (G/H) contains each irreducible representation of G at most finitely many times if the number of H-orbits on G/P is finite.
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RECENT DEVELOPMENTS IN THE THEORY OF MULTIPLE ZETA VALUES IN POSITIVE CHARACTERISTIC (Algebraic Number Theory and Related Topics)

open access: yesRECENT DEVELOPMENTS IN THE THEORY OF MULTIPLE ZETA VALUES IN POSITIVE CHARACTERISTIC (Algebraic Number Theory and Related Topics)
Thakur introduced MZV's in positive characteristic as analogues of the classical multiple zeta values of Euler. This manuscript reports our recent results on these values in [33, 34, 38]. This text relates to the presentation given by the author at the ”Algebraic Number Theory and Related Topics” workshop, which took place at the Research Institute for
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ON THE sl₂-ALGEBRA OF FORMAL MULTIPLE EISENSTEIN SERIES (Algebraic Number Theory and Related Topics)

open access: yesON THE sl₂-ALGEBRA OF FORMAL MULTIPLE EISENSTEIN SERIES (Algebraic Number Theory and Related Topics)
In this survey article we summarize the results of [BIM] in which the authors introduced the algebra of formal multiple Eisenstein. This algebra is motivated by the classical multiple Eisenstein series, introduced by Gangl-Kaneko-Zagier as a hybrid of classical Eisenstein series and multiple zeta values.
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On the special values of certain multiple Dirichlet series (Analytic Number Theory and Related Topics)

open access: yesOn the special values of certain multiple Dirichlet series (Analytic Number Theory and Related Topics)
本稿では、2018年10月29日(月)から31日(水)まで行われた研究集会「解析的整数論とその周辺」において講演した「ある種の多童Dirichlet級数の特殊値について」の結果を紹介する。
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Artin style characterizations of the multiple gamma and sine functions (Analytic Number Theory and Related Topics)

open access: yesArtin style characterizations of the multiple gamma and sine functions (Analytic Number Theory and Related Topics)
E. Artinによる積公式を用いたガンマ函数の特徴付けを多重化し,多菫ガンマ函数や多重三角函数といった多重特殊函数の特徴付けを与える.
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Noether's problem and rationality problem for multiplicative invariant fields: a survey (Algebraic Number Theory and Related Topics 2016)

open access: yesNoether's problem and rationality problem for multiplicative invariant fields: a survey (Algebraic Number Theory and Related Topics 2016)
In this paper, we give a brief survey of recent developments on Noether's problem and rationality problem for multiplicative invariant fields including author's recent papers Hoshi [Hos15] about Noether's problem over Q, Hoshi, Kang and Kunyavskii [HKK13], Chu, Hoshi, Hu and Kang [CHHK15], Hoshi [Hos16] and Hoshi, Kang and Yamasaki [HKY16] about ...
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