Low-lying zero densities for Hecke-Maass L-functions over class-number-one imaginary quadratic fields match orthogonal random matrix ensembles in the level and eigenvalue aspects.
Theory of Fundamental Bessel Functions of High Rank
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this article, we shall study fundamental Bessel functions for $\mathrm{GL}_n(\mathbb{F})$ arising from the Vorono\"i summation formula for any rank $n$ and field $\mathbb{F} = \mathbb{R}$ or $\mathbb{C}$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. We shall prove the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
fields
math.NT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Low-lying zeros of $L$-functions for Maass forms over imaginary quadratic fields
Low-lying zero densities for Hecke-Maass L-functions over class-number-one imaginary quadratic fields match orthogonal random matrix ensembles in the level and eigenvalue aspects.