Shintani – Barnes zeta and gamma functions

  title={Shintani – Barnes zeta and gamma functions},
  author={Eduardo Friedman and Simon M. Ruijsenaars and Takahiro Kawai},
We show that Shintani’s work on multiple zeta and gamma functions can be simplified and extended by exploiting difference equations. We re-prove many of Shintani’s formulas and prove several new ones. Among the latter is a generalization to the Shintani–Barnes gamma functions of Raabe’s 1843 formula R 1 0 log GðxÞ dx 1⁄4 log ffiffiffiffiffi 2p p ; and a further generalization to the Shintani zeta functions. These explicit formulas can be interpreted as ‘‘vanishing period integral’’ side… CONTINUE READING

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Showing 1-10 of 18 references

A proof of the classical Kronecker limit formula

  • T. Shintani
  • Tokyo J. Math. 3 (1980) 191–199. ARTICLE IN…
  • 2004

Special functions defined by analytic difference equations

  • S.N.M. Ruijsenaars
  • in: J. Bustoz, M. Ismail, S. Suslov (Eds…
  • 2001

On Barnes’ multiple zeta and gamma functions

  • S.N.M. Ruijsenaars
  • Adv. in Math. 156
  • 2000
2 Excerpts

Special Functions

  • G. Andrews, R. Askey, R. Roy
  • Cambridge University Press, Cambridge
  • 1999

First order analytic difference equations and integrable quantum systems

  • S.N.M. Ruijsenaars
  • J. Math. Phys. 38
  • 1997
2 Excerpts

Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques

  • P. Cassou-Noguès
  • Invent. Math. 51
  • 1979
1 Excerpt

On certain ray class invariants of real quadratic fields

  • T. Shintani
  • J. Math. Soc. Japan 30
  • 1978

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