turkmath.org

In this talk I will start by describing a certain subset of real numbers which contain all the numbers which are of interest to arithmeticians. These numbers are called periods, and they form a countable set and in principle are much more easy to handle than a general real number. Then I will specialize to a certain subset of periods which are of mixed Tate type. The ones which have good reduction for all primes have periods called multi-zeta values, which were first defined by Euler. The remainder of the talk will be about a p-adic version of these numbers called p-adic multi-zeta values. There are p-adic periods of the unipotent fundamental group of the thrice punctured line. They turn out to give all the p-adic periods of mixed Tate motives over Z. I will give an explicit series representation of these values in all depths. The new tool is a certain regularization trick for p-adic series.