Geometric Gamma values and zeta values in positive characteristic

Details Geometric Gamma values and zeta values in positive characteristic Geometric Gamma values and zeta values in positive characteristic

2009-05-18

arxiv.org/abs/0905.2876v2

Int. Math. Res. Not. IMRN 2010, no. 8, 1432-1455

Mathematics

Number Theory

15 pages

Scientific paper

In analogy with values of the classical Euler Gamma-function at rational numbers and the Riemann zeta-function at positive integers, we consider Thakur's geometric Gamma-function evaluated at rational arguments and Carlitz zeta-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 Gamma-function and from the Euler-Carlitz relations and Frobenius p-th power relations of the zeta-function.

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