Modified Bessel Functions in Analytic Number Theory

2023/03/04 by Berndt, Bruce C., Dixit, Atul, Gupta, Rajat +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.02520

Abstract

The modified Bessel functions K_ν(z), or, for brevity, K-Bessel functions, arise at key places in analytic number theory. In particular, they appear in beautiful arithmetic identities. A survey of these arithmetical identities and their appearances in number theory is provided.

Related

• Series Representation of the Modified Bessel Functions
• Two General Series Identities Involving Modified Bessel Functions and a Class of Arithmetical Functions
• The generalized modified Bessel function K_z,w(x) at z=1/2 and Humbert functions
• A class of identities relating Whittaker and Bessel functions
• A note on a modified Bessel function integral