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National Center for Theoretical Science, Taiwan
Title: Determination of algebraic relations among special gamma values and zeta values in positive characteristic
Abstract: As analogue to the classical Euler gamma function at rational numbers and the Riemann zeta function at positive integers, we consider Thakur's geometric gamma function at rational functions and Carlitz zeta values at positive integers. We prove that among these special values put together, all the algebraic relations are those from the standard functional equations of the gamma function, the Euler-Carlitz relations and the Frobenius p-th power relations (joint work with Matthew A. Papanikolas and Jing Yu)