Vaibhav Suvagiya

Parity families and a kernel-averaged L-function for near-Ramanujan signings

For a signing $\sigma$ of a $d$-regular graph, the spectrum of $A_\sigma$ depends only on the signs of cycles. We study the affine $\mathbb F_2$ family of signings making every short even cycle unbalanced, and show that averaging over it converts the sign problem of the Bilu-Linial conjecture into a counting problem: a...