An effective criterion for Eulerian multizeta values in positive characteristic
Abstract
Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present paper we establish an effective criterion for Eulerian multizeta values, which characterizes when a multizeta value is a rational multiple of a power of the Carlitz period. The resulting "tmotivic" algorithm can tell whether any given multizeta value is Eulerian or not. We also prove that if zeta_A(s_1,...,s_r) is Eulerian, then zeta_A(s_2,...,s_r) has to be Eulerian. When r=2, this was conjectured (and later on conjectured for arbitrary r) by Lara Rodriguez and Thakur for the zetalike case from numerical data. Our methods apply equally well to values of Carlitz multiple polylogarithms at algebraic points and zetalike multizeta values.
 Publication:

arXiv eprints
 Pub Date:
 November 2014
 arXiv:
 arXiv:1411.0124
 Bibcode:
 2014arXiv1411.0124C
 Keywords:

 Mathematics  Number Theory;
 11R58;
 11J93 (Primary) 11G09;
 11M32;
 11M38 (Secondary)
 EPrint:
 32 pages