Linear relations among double zeta values in positive characteristic

2015/10/22 by Chang, Chieh-Yu
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1510.06519

Abstract

The study of this paper is inspired by the conjecture of Zagier on the explicit dimension formula for the space of the same weight double zeta values in terms of the dimension of cusp forms for SL₂(Z). Our main result is to devise an effective criterion for computing the dimension of the same weight double zeta values over a rational function field F_q(theta) in positive characteristic. Contrary to the Zagier's conjecture, the analogue of Zagier's conjectural dimension provides a lower bound for the dimension of the double zeta values when the weight is A-even.

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