The paper by **Sandro Mattarei ****and Roberto Tauraso, ***From generating series to polynomial congruences**, *has been accepted for publication in** Journal of Number Theory.**

(You may find the final version in preprint form at https://arxiv.org/pdf/1703.02322.pdf.)

*Abstract*: Consider an ordinary generating function , of an integer sequence of some combinatorial relevance, and assume that it admits a closed form . Various instances are known where the corresponding truncated sum , with a power of a prime , also admits a closed form representation when viewed modulo . Such a representation for the truncated sum modulo frequently bears a resemblance with the shape of despite being typically proved through independent arguments. One of the simplest examples is the congruence being a finite match for the well-known generating function . We develop a method which allows one to directly infer the closed-form representation of the truncated sum from the closed form of the series for a significant class of series involving central binomial coefficients. In particular, we collect various known such series whose closed-form representation involves polylogarithms , and after supplementing them with some new ones we obtain closed-forms modulo for the corresponding truncated sums, in terms of finite polylogarithms .

%d bloggers like this:

Reblogged this on Maths & Physics News.

LikeLike