New paper accepted in Journal of Number Theory

Charlotte Scott Centre for Algebra

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

(You may find the final version in preprint form at

Abstract: Consider an ordinary generating function $latex sum_{k=0}^{infty}c_kx^k$, of an integer sequence of some combinatorial relevance, and assume that it admits a closed form $latex C(x)$. Various instances are known where the corresponding truncated sum $latex sum_{k=0}^{q-1}c_kx^k$, with $latex q$ a power of a prime $latex p$, also admits a closed form representation when viewed modulo $latex p$. Such a representation for the truncated sum modulo $latex p$ frequently bears a resemblance with the shape of $latex C(x),$ despite being typically proved through independent arguments. One of the simplest examples is the congruence $latex sum_{k=0}^{q-1}binom{2k}{k}x^kequiv(1-4x)^{(q-1)/2}pmod{p}$ being a finite match for the well-known generating function $latex sum_{k=0}^inftybinom{2k}{k}x^k= 1/sqrt{1-4x}$. We develop a method which…

View original post 71 more words

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

© School of Mathematics and Physics, University of Lincoln, Brayford Pool, Lincoln, LN6 7TS, United Kingdom
%d bloggers like this: