On \(p\)-adic multiple zeta and log gamma functions

DOI10.1016/J.JNT.2011.01.010zbMath1245.11113OpenAlexW2001035846MaRDI QIDQ533815

Paul Thomas Young, Brett A. Tangedal

Publication date: 6 May 2011

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.01.010

zbMATH Keywords

multiple gamma functions\(p\)-adic analysisVolkenborn integralBarnes multiple zeta functionsdiamond function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Related Items (17)

The \(p\)-adic analytic Dedekind sums ⋮ A research on the recursive value and general terms of the analogue Euler zeta function on positive integers ⋮ Explicit computation of Gross-Stark units over real quadratic fields ⋮ A note on p-adic Raabe formulas ⋮ Polylogarithmic zeta functions and their p-adic analogues ⋮ A construction of \(p\)-adic Hurwitz-Lerch \(L\)-function ⋮ Absolute series for higher Euler constants ⋮ On \(p\)-adic Hurwitz-type Euler zeta functions ⋮ On \(p\)-adic analogue of Weil's elliptic functions according to Eisenstein ⋮ The \((S, \{2 \})\)-Iwasawa theory ⋮ Unnamed Item ⋮ Infinite order linear differential equation satisfied by \(p\)-adic Hurwitz-type Euler zeta functions ⋮ Fundamentals of \(p\)-adic multiple \(L\)-functions and evaluation of their special values ⋮ The \(p\)-adic Arakawa-Kaneko-Hamahata zeta functions and poly-Euler polynomials ⋮ A two-variable generalization of the Kummer-Malmstén formula for the logarithm of the double gamma and double sine functions ⋮ On \(p\)-adic Diamond-Euler log gamma functions ⋮ The \(p\)-adic Arakawa-Kaneko zeta functions and \(p\)-adic Lerch transcendent

Cites Work

• Continued fractions, special values of the double sine function, and Stark units over real quadratic fields
• Congruences for Bernoulli, Euler, and Stirling numbers
• Applications arithmétiques de l'étude des valeurs aux entiers négatifs des séries de Dirichlet associées à un polynôme
• On a \(p\)-adic analogue of Shintani's formula
• On <i>p</i>-adic absolute CM-periods I
• The p-Adic Log Gamma Function and p-Adic Euler Constants
• Multiple sine functions
• Number Theory
• On Barnes' multiple zeta and gamma functions
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