Theory of Fundamental Bessel Functions of High Rank (Memoirs of the American Mathematical Society)

About the Author Zhi Qi, The Ohio State University, Columbus, OH Product Description In this article, the author studies fundamental Bessel functions for $\mathrm{GL}_n(\mathbb F)$ arising from the Voronoi 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 this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.