A result on the $c_2$ invariant for powers of primes

Abstract

The $c_2$ invariant is an arithmetic graph invariant related to quantum field theory. We give a relation modulo $p$ between the $c_2$ invariant at $p$ and the $c_2$ invariant at $p^s$, providing evidence for a conjecture of Schnetz. The key result is a relation modulo $p$ between certain coefficients of powers of products of particularly nice polynomials.Comment: 16 pages, edits according to referee comments including extracting the main result at the level of polynomial