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

Maria S. Esipova; Karen Yeats

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

Combinatorics 2023-03-30 v5 High Energy Physics - Theory Mathematical Physics math.MP

Authors: Maria S. Esipova , Karen Yeats

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 $p^s$ by proving a relation modulo $p$ between certain coefficients of powers of products of particularly nice polynomials. The relation at the level of the $c_2$ invariant provides evidence for a conjecture of Schnetz.

Keywords

c2 invariant arithmetic graph invariant modular relation prime powers polynomial coefficients quantum field theory Schnetz conjecture

Cite

@article{arxiv.2206.06835,
  title  = {A result on the $c_2$ invariant for powers of primes},
  author = {Maria S. Esipova and Karen Yeats},
  journal= {arXiv preprint arXiv:2206.06835},
  year   = {2023}
}

Comments

16 pages, some further edits according to referee comments

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

Abstract

Keywords

Cite

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