Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions

2014/08/25 by Zhi Qi, Qi, Zhi
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1408.5652

openalex publication_date 2014/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we introduce a new category of special functions called fundamental Bessel functions arising from the Voronoi summation formula for GL_n (ℝ). The fundamental Bessel functions of rank one and two are the oscillatory exponential functions e^{± i x} and the classical Bessel functions respectively. The main implements and subjects of our study of fundamental Bessel functions are their formal integral representations and Bessel equations.

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