CiNii Articles - special value of zeta function

1

Hasse-Weil zeta functions of character varieties of hyperbolic 3-manifolds (Algebraic Number Theory and Related Topics 2017)

Harada Shinya

… The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. …

数理解析研究所講究録別冊 = RIMS Kokyuroku Bessatsu (B83), 3-10, 2020-10

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2

On the density function for the value-distribution of automorphic L-functions

Matsumoto Kohji , Umegaki Yumiko

… The Bohr–Jessen limit theorem is a probabilistic limit theorem on the value-distribution of the Riemann zeta-function in the critical strip. … Moreover their limit measure can be written as an integral involving a certain density function. …

Journal of Number Theory (198), 176-199, 2019-05

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3

On the values at zero of partial zeta functions for ray classes of a real quadratic field(2)

Yamashita Hiroshi

… Let o: be an integer of k and m be a positive rational integer. … Denote by ((a, (m), s) be a partial zeta function associated to a ray class a containing the principal ideal (α) defined with a conductor (m). …

金沢大学人間社会研究域学校教育系紀要 = Bulletin of the Faculty of Education (9), 13-22, 2017

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4

On the values at zero of partial zeta functions for ray classes of a real quadratic field

YAMASHITA Hiroshi

… Let a be an integer of k and m be a positive rational integer. … Denote by ( ( (a), ( m), s) be a partial zeta function associated to a ray class containing the principal ideal (a) defined with a conductor (m). …

金沢大学人間社会学域学校教育学類紀要 (8), 13-24, 2016

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5

Special values of zeta functions of varieties over finite fields via higher Chow groups : a survey (Algebraic Number Theory and Related Topics 2013) [in Japanese]

Miyazaki Hiroyasu

… The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.本稿の目的は, 有限体上の(特異な)多様体のゼータ関数の特殊値を, 高次チャウ群を用いて記述する筆者の結果([15])を概説することである. …

RIMS Kokyuroku Bessatsu (B53), 103-115, 2015-09

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6

N.コブリッツ（上田勝・浜畑芳紀訳）：楕円曲線と保型形式，シュプリンガー・ジャパン，2006年，371ページ． [in Japanese]

Sakata Hiroshi

SUGAKU 66(1), 96-100, 2014

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7

THE BARNES G-FUNCTION AND THE CATALAN CONSTANT

WANG Xiaohan

… It is the special value at s=2 of the Dirichlet L-function associated with the Gaussian field with its character odd. …

Kyushu Journal of Mathematics 67(1), 105-116, 2013

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8

A Generalization of the Artin-Tate Formula for Fourfolds

… We give a new formula for the special value at s = 2 of the Hasse-Weil zeta function for smooth projective fourfolds under some assumptions (the Tate & Beilinson conjecture and the finite generation of the Chow group CH2(X). …

Journal of mathematical sciences, the University of Tokyo 17(4), 419-453, 2011-03-29

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9

A Generalization of the Artin-Tate Formula for Fourfolds

Kohmoto Daichi

… We give a new formula for the special value at s = 2 of the Hasse-Weil zeta function for smooth projective fourfolds under some assumptions (the Tate & Beilinson conjecture and the finite generation of the Chow group CH2(X). …

Journal of mathematical sciences, the University of Tokyo 17(4), 419-453, 2011-03-29

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10

The best constant of Sobolev inequality corresponding to Dirichlet-Neumann boundary value problem for $(-1)^M(d/dx)^{2M}$}

Yamagishi Hiroyuki

… We clarified the variational meaning of the special values $\zeta(2M)\ (M=1,2,3,\cdots)$ of Riemann zeta function $\zeta(s)$. … These are essentially the best constant of Sobolev inequality. … In the background we consider Dirichlet-Neumann boundary value problem for a differential operator $(-1)^M(d/dx)^{2M}$. …

Hiroshima mathematical journal 39(3), 421-442, 2009-11
11

A remark on the Riccati equation associated with a hypergeometric equation

青木貴史 , 王梟涵

… This construction of solution provides a point of view about the Gauss formula which gives the special value of hypergeometric function at the unit. …

近畿大学理工学部研究報告 (45), 1-3, 2009-09

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12

Riemann zeta function and the best constants of three series of Sobolev inequalities(Theory,Applied Integrable Systems,<Special Issue>Joint Symposium of JSIAM Activity Groups 2007) [in Japanese]

Kametaka Yoshinori , Yamagishi Hiroyuki , Watanabe Kohtaro , Nagai Atsushi , Takemura Kazuo

リーマンゼータ関数の偶数における値ζ(2M)(M=1,2,3,…)に変分学的意味付けを行った.それは3系列のソボレフ不等式の最良定数である.背景には簡単な常微分作用素に対する周期境界条件,ディリクレ境界条件,ノイマン境界条件をともなった3種類の境界値問題がある.グリーン関数G(x,y)をベルヌーイ多項式で構成できる.G(x,y)のxにかんするソボレフエネルギーはその対角線値G(y,y)であり,その …

Transactions of the Japan Society for Industrial and Applied Mathematics 18(1), 29-40, 2008

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13

RIEMANN ZETA FUNCTION, BERNOULLI POLYNOMIALS AND THE BEST CONSTANT OF SOBOLEV INEQUALITY

KAMETAKA YOSHINORI , YAMAGISHI HIROYUKI , WATANABE KOHTARO , NAGAI ATSUSHI , TAKEMURA KAZUO

… Green function for periodic boundary value problem of 2M-th order ordinarydifferential equation is found by symmetric orthogonalization method undera suitable solvability condition. … As an application, the best constants and the bestfunctions of the Sobolev inequalities in a certain series of Hilbert spaces are found andexpressed by means of the well-known Bernoulli polynomials. …

Scientiae Mathematicae Japonicae 65(3), 333-359, 2007-05-01

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14

APÉRY-LIKE NUMBERS ARISING FROM SPECIAL VALUES OF SPECTRAL ZETA FUNCTIONS FOR NON-COMMUTATIVE HARMONIC OSCILLATORS

KIMOTO Kazufumi , WAKAYAMA Masato

… We derive an expression for the value $ \zeta_Q (3) $ of the spectral zeta function $ \zeta_Q (s) $ for the non-commutative harmonic oscillator using a Gaussian hypergeometric function. …

Kyushu Journal of Mathematics 60(2), 383-404, 2006

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15

A special value of the spectral zeta function of the non-commutative harmonic oscillators (Automorphic forms on $Sp$(2,$\mathbf{R}$) and $SU$(2,2) III)

Ochiai Hiroyuki

RIMS Kokyuroku 1421, 38-43, 2005-04

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16

ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF INTEGRAL WEIGHT BELONGING TO KOHNEN'S SPACES AND THE CRITICAL VALUES OF ZETA FUNCTIONS

KOJIMA HISASHI , TOKUNO YASUSHI

… The purpose of this paper is to derive a generalization of Kohnen-Zagier's results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces, and to refine our previous results concerning Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces. …

Tohoku Mathematical Journal, Second Series 56(1), 125-145, 2004

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17

Remark on Fourier coefficients of modular forms of half integral weight belonging to Kohnen's spaces

KOJIMA Hisashi

… purpose of this paper is to derive that the square of Fourier coefficients a(n) at a square free positive integer n of modular forms f of half integral weight belonging to Kohnen's spaces of arbitrary odd level and of arbitrary primitive character is essentially equal to the critical value of the zeta function …

Journal of the Mathematical Society of Japan 51(3), 715-730, 1999-07

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18

Conductance of potassium iodide in supercooled water.

Nakahara Masaru , Zenke Masanobu

… The conductance of potassium iodide was measured in water as a function of concentration (between 2×10−3 … The effect of temperature on the mobility of such halide ions as I− …

Bulletin of the Chemical Society of Japan 60(2), 493-496, 1987

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19

Congruences of cusp forms and special value of their zeta function s

HIDA H.

Invent. Math. 63, 225-261, 1981

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