2 results
A result on the
$c_2$ invariant for powers of primes
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 66 / Issue 4 / December 2023
- Published online by Cambridge University Press:
- 24 April 2023, pp. 1164-1178
- Print publication:
- December 2023
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
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.
A Special Case of Completion Invariance for the c2 Invariant of a Graph
-
- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 6 / 01 December 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1416-1435
- Print publication:
- 01 December 2018
-
- Article
-
- You have access
- Export citation
-
The
${{c}_{2}}$ invariant is an arithmetic graph invariant defined by Schnetz. It is useful for understanding Feynman periods. Brown and Schnetz conjectured that the ${{c}_{2}}$ invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the ${{c}_{2}}$ invariant in the case where we are over the field with 2 elements and the completed graph has an odd number of vertices. The methods involve enumerating certain edge bipartitions of graphs; two different constructions are needed.
