Geometric Gamma Values and Zeta Values in Positive Characteristic Academic Article uri icon

abstract

  • In analogy with values of the classical Euler Γ-function at rational numbers and the Riemann ζ-function at positive integers, we consider Thakur's geometric Γ-function evaluated at rational arguments and Carlitz ζ-values at positive integers. We prove that, when considered together, all of the algebraic relations among these special values arise from the standard functional equations of the Γ-function and from the Euler-Carlitz relations and Frobenius p-th power relations of the ζ-function. © 2009 The Author.

author list (cited authors)

  • Chang, C. Y., Papanikolas, M. A., & Yu, J.

citation count

  • 1

publication date

  • November 2009