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Theory of Fundamental Bessel Functions of High Rank
About this Title
Zhi Qi
Publication: Memoirs of the American Mathematical Society
Publication Year:
2020; Volume 267, Number 1303
ISBNs: 978-1-4704-4325-2 (print); 978-1-4704-6405-9 (online)
DOI: https://doi.org/10.1090/memo/1303
Published electronically: January 13, 2021
Keywords: Hankel transforms,
Bessel kernels,
Bessel functions,
formal integral representations,
Bessel differential equations
Table of Contents
Chapters
- Introduction
- 1. Hankel Transforms and Bessel Kernels
- 2. Analytic Theory of Bessel Functions
- 3. Bessel Kernels
- 4. Hankel Transforms and Bessel Kernels in Representation Theory
Abstract
In this article, we shall study fundamental Bessel functions for ${\mathrm {GL}}_n({\mathbb {F}})$ arising from the Voronoï\hskip3 pt 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.- Valentin Blomer, Subconvexity for twisted $L$-functions on $\textrm {GL}(3)$, Amer. J. Math. 134 (2012), no. 5, 1385–1421. MR 2975240, DOI 10.1353/ajm.2012.0032
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