A VARIATION OF EULER′S APPROACH TO VALUES OF THE RIEMANN ZETA FUNCTION

Masanobu Kaneko, Nobushige Kurokawa, Masato Wakayama

Type: Article

Publication Date: 2003-01-01

Citations: 76

DOI: https://doi.org/10.2206/kyushujm.57.175

Abstract

An elementary method of computing the values at negative integers of the Riemann zeta function is presented. The principal ingredient is a new q-analogue of the Riemann zeta function. We show that for any argument other than 1 the classical limit of this q-analogue exists and equals the value of the Riemann zeta.

Locations

arXiv (Cornell University) - View
QIR (Kyushu University Institutional Repository) (Kyushu University) - View - PDF
Kyushu Journal of Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+	A variation of Euler's approach to values of the Riemann zeta function	2002	Masanobu Kaneko Nobushige Kurokawa Masato Wakayama
+ PDF Chat	A q-analogue for Euler’s evaluations of the Riemann zeta function	2018	Ankush Goswami
+	An elementary and real approach to values of the Riemann zeta function	2008	Armen Bagdasaryan
+	An elementary and real approach to values of the Riemann zeta function	2008	Armen Bagdasaryan
+ PDF Chat	An elementary and real approach to values of the Riemann zeta function	2010	Armen Bagdasaryan
+	An Elementary and Real Approach to Values of the	2009	Armen Bagdasaryan
+	A q-Analog of Euler’s Reduction Formula for the Double Zeta Function	2013	David M. Bradley Xia Zhou
+ PDF Chat	A simple approach to the analytic continuation and values at negative integers for Riemann’s zeta function	1981	David Goss
+	A Simple Approach to the Analytic Continuation and Values at Negative Integers for Riemann's Zeta-Function	1981	David A. Goss
+	A generalization of the riemann zeta-function	1989	K. Ramachandra И. В. Волович
+	Classical values of Zeta, as simple as possible but not simpler	2023	Olga Holtz
+	On q-analogues of Riemann's zeta function	2001	Ivan Cherednik
+	The Riemann Zeta Function	2019	Sebastián Carrillo Santana
+ PDF Chat	Analytic continuation of Riemann’s zeta function and values at negative integers via Euler’s transformation of series	1994	Jonathan Sondow
+ PDF Chat	Analytic Continuation of Riemann's Zeta Function and Values at Negative Integers Via Euler's Transformation of Series	1994	Jonathan Sondow
+	A new generalization of the Riemann zeta function and its difference equation	2011	Asghar Qadir Tassaddiq Asifa Chaudhry Muhammad
+	A note on riemann's zeta-function	1975	J. Lune van de
+	A note on riemann's zeta-function	1975	J. van deLune
+	A study of the Riemann zeta function	2017	Yochay Jerby
+	Calculating zeros of a q-zeta function numerically	1998	Ivan Cherednik

Works That Cite This (76)

Action	Title	Year	Authors
+ PDF Chat	Uniform Approach to Double Shuffle and Duality Relations of Various q-Analogs of Multiple Zeta Values via Rota–Baxter Algebras	2020	Jianqiang Zhao
+ PDF Chat	Some Double q-Series by Telescoping	2023	Kwang-Wu Chen
+	Zeta Functions for the Spectrum of the Non-Commutative Harmonic Oscillators	2005	Takashi Ichinose Masato Wakayama
+ PDF Chat	Multiple q-zeta functions and multiple q-polylogarithms	2007	Jianqiang Zhao
+	Connection problems of Fuchsian equations and relations for multiple L-values	2004	順一奥田
+ PDF Chat	A Restricted Sum Formula for a q-Analogue of Multiple Zeta Values	2012	Yoshihiro Takeyama
+ PDF Chat	Derivations on the algebra of multiple harmonic q-series and their applications	2019	Yoshihiro Takeyama
+	A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-analogue of the Bailey–Borwein–Bradley identity	2011	Kh. Hessami Pilehrood Tatiana Hessami Pilehrood
+ PDF Chat	Evaluations of multiple Dirichlet L-values via symmetric functions	2009	Yoshinori Yamasaki
+ PDF Chat	Renormalization of multiple q-zeta values	2008	Jianqiang Zhao

Works Cited by This (4)

Action	Title	Year	Authors
+	Quantum groups and zeta-functions	1994	Kimio Ueno Michitomo Nishizawa
+	Über die Bestimmung Dirichletscher Reihen durch ihre Funktionalgleichung	1936	E. Hecke
+	A note on q-analogues of the Dirichlet series and q-Bernoulli numbers	1991	Hirofumi Tsumura
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown