2023/01/17 by Jack Buttcane, Buttcane, Jack
Mathematics · #33C70 #42B37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11F72 #Secondary 11F55
paper · pdf · doi:10.48550/arxiv.2301.06934
openalex publication_date 2023/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of the Kuznetsov trace formula, we outline the theory of the Bessel functions on GL(n) as a series of conjectures designed as a blueprint for the construction of Kuznetsov-type formulas with given ramification at infinity. We are able to prove one of the conjectures at full generality on GL(n) and most of the conjectures in the particular case of the long Weyl element; as with previous papers, we give some unconditional results on Archimedean Whittaker functions, now on GL(n) with arbitrary weight. We expect the heuristics here to apply at the level of real reductive groups. In an appendix, we make good progress toward series and integral representations of GL(4) Bessel functions by proving several of the conjectures for GL(4).