q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function

DOI10.1515/FORUM.2008.001zbMath1205.11095arXivmath/0402135OpenAlexW2072631358MaRDI QIDQ5451983

Yoshinori Yamasaki, Masato Wakayama, Kenichi Kawagoe

Publication date: 27 March 2008

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402135

zbMATH Keywords

\(q\)-analogue of the Dirichlet \(L\)-functionsanalogue of the Riemann hypothesis for a crystal zeta functioncrystal limit behavior of zeros

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (12)

On \(q\)-analogues of the Barnes multiple zeta functions ⋮ Evaluations of multiple Dirichlet \(L\)-values via symmetric functions ⋮ Integral representations of \(q\)-analogues of the Hurwitz zeta function ⋮ Families of Twisted Bernoulli Numbers, Twisted Bernoulli Polynomials, and Their Applications ⋮ On q-analogs of zeta functions associated with a pair of q-analogs of Bernoulli numbers and polynomials ⋮ A twisted spectral triple for quantum \(SU(2)\) ⋮ \(q\)-deformations of statistical mechanical systems and motives over finite fields ⋮ Hermite's formulas for \(q\)-analogues of Hurwitz zeta functions ⋮ Multiple \(q\)-zeta functions and multiple \(q\)-polylogarithms ⋮ Unnamed Item ⋮ Zeta functions of \(q\)-perfect numbers ⋮ Zeta functions for the spectrum of the non-commutative harmonic oscillators

Cites Work

• \(q\)-analogue of Riemann's \(\zeta\)-function and \(q\)-Euler numbers
• A note on \(q\)-analogues of Dirichlet series
• Generalized zeta regularizations, quantum class number formulas, and Appell's \(O\)-functions
• On 𝑞-analogues of the Euler constant and Lerch’s limit formula
• A VARIATION OF EULER′S APPROACH TO VALUES OF THE RIEMANN ZETA FUNCTION
• On \(q\)-analogues of Riemann's zeta function

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