Zeta-like Multizeta Values for higher genus curves

Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields

We explain work on the arithmetic of Gamma and Zeta values for function fields. We will explore analogs of the gamma and zeta functions, their properties, functional equations, interpolations, their special values, their connections with periods of Drinfeld modules and t-motives, algebraic relations they satisfy and various methods showing that there are no more relations between them. We also ...

Shuffle Relations for Function Field Multizeta Values

Despite the failure of naive analogs of the sum shuffle or the integral shuffle relations, we prove the existence of ‘shuffle’ relations for the multizeta values (for a general A, with a rational place at infinity) introduced [T04] by the author in the function field context. This makes the Fp-span of the multizeta values into an algebra. We effectively determine and prove all the Fp-coefficien...

Higher Order Shuffle Regularization for Multiple Zeta Values

We study the higher order shuffle regularization for multiple zeta values and define higher order regularized shuffle relations. We find that higher order regularized shuffle relations can be deduced from the group-like property of the Drinfel’d associator.

Applications of Multizeta Values to Mahler Measure

These notes correspond to a mini-course taught by the author during the program “PIMS-SFU undergraduate summer school on multiple zeta values: combinatorics, number theory and quantum field theory”. Please send any comments or corrections to the author at [email protected]. 1. Primes, Mahler Measure, and Lehmer’s question We start our study by discussing prime numbers. First consider the ...

Euler systems on Drinfeld modular curves and zeta values