Hurwitz zeta functions and Ramanujan's identity for odd zeta values

被引：1
|
作者：
Chavan, Parth [1 ]
机构：
[1] Euler Circle, Palo Alto, CA 94306 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 02期
关键词：
Hurwitz zeta function; Ramanujan's formula for odd zeta; values; Dirichlet series;
D O I：
10.1016/j.jmaa.2023.127524
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the Hurwitz zeta function, generalizing that associated to Ramanujan's identity. We also derive several infinite families of identities analogous to Ramanujan's formula. & COPY; 2023 Elsevier Inc. All rights reserved.
引用
收藏
页数：20
相关论文
共 50 条
  • [1] Dirichlet series under standard convolutions: variations on Ramanujan’s identity for odd zeta values
    Parth Chavan
    Sarth Chavan
    Christophe Vignat
    Tanay Wakhare
    The Ramanujan Journal, 2022, 59 : 1245 - 1285
  • [2] Dirichlet series under standard convolutions: variations on Ramanujan's identity for odd zeta values
    Chavan, Parth
    Chavan, Sarth
    Vignat, Christophe
    Wakhare, Tanay
    RAMANUJAN JOURNAL, 2022, 59 (04): : 1245 - 1285
  • [3] A DIRICHLET CHARACTER ANALOGUE OF RAMANUJAN’S FORMULA FOR ODD ZETA VALUES
    Gupta, Anushree
    Jamal, M.D. Kashif
    Karak, Nilmoni
    Maji, Bibekananda
    arXiv, 2023,
  • [4] A Dirichlet character analogue of Ramanujan's formula for odd zeta values
    Gupta, Anushree
    Jamal, Md Kashif
    Karak, Nilmoni
    Maji, Bibekananda
    ADVANCES IN APPLIED MATHEMATICS, 2024, 158
  • [5] Recent developments pertaining to Ramanujan's formula for odd zeta values
    Dixit, Atul
    EXPOSITIONES MATHEMATICAE, 2024, 42 (05)
  • [6] Asymptotic expansions of multiple zeta functions and power mean values of Hurwitz zeta functions
    Egami, S
    Matsumoto, K
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2002, 66 : 41 - 60
  • [7] Odd zeta motive and linear forms in odd zeta values
    Dupont, Clement
    Zagier, Don
    COMPOSITIO MATHEMATICA, 2018, 154 (02) : 342 - 379
  • [8] Multiple Hurwitz zeta functions
    Murty, M. Ram
    Sinha, Kaneenika
    MULTIPLE DIRICHLET SERIES, AUTOMORPHIC FORMS, AND ANALYTIC NUMBER THEORY, 2006, 75 : 135 - +
  • [9] DISCRETE MEAN-VALUES OF HURWITZ ZETA-FUNCTIONS
    KATSURADA, M
    MATSUMOTO, K
    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1993, 69 (06) : 164 - 169
  • [10] A New Family of Zeta Type Functions Involving the Hurwitz Zeta Function and the Alternating Hurwitz Zeta Function
    Kim, Daeyeoul
    Simsek, Yilmaz
    MATHEMATICS, 2021, 9 (03) : 1 - 11
12345