A Combinatorial Approach to Mixed Ratios of Characteristic Polynomials

Autor:	Riedtmann, Helen
Rok vydání:	2018
Předmět:	Mathematics - Combinatorics Mathematics - Number Theory 05E05 11M50 15B52 (Primary)
Druh dokumentu:	Working Paper
Popis:	We provide a combinatorial derivation of an asymptotic formula for averages of mixed ratios of characteristic polynomials over the unitary group, where mixed ratios are products of ratios and/or logarithmic derivatives. Our proof of this formula is a generalization of Bump and Gamburd's elegant combinatorial proof of Conrey, Forrester and Snaith's formula for averages of ratios of characteristic polynomials over the unitary group. One application of this formula is an asymptotic expression for sums over zeros of a random characteristic polynomial from the unitary group, which we call an explicit formula for eigenvalues in an analogy to what is called an explicit formula in the context of $L$-functions. Comment: 38 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.07261 Zobrazit plný text záznamu View this record from Arxiv