2022/06/25 by Paul Buckingham, Buckingham, Paul · 1 citation
Mathematics · #11S80 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11S80
paper · pdf · doi:10.48550/arxiv.2206.12726
38 pages. This version includes an integral-transform formula for the $p$-adic incomplete Gamma functions. It also corrects some typos and clarifies the text in several places
openalex publication_date 2022/06/25 · openalex created_date 2022/06/30 · arxiv created 2022/07/15 · arxiv updated 2022/07/18 · openalex updated_date 2026/07/28
We introduce an automorphism S of the space C(ℤp,ℂp) of continuous functions ℤp → ℂp and show that it can be used to give an alternative construction of the p-adic incomplete Γ-functions recently introduced by O'Desky and Richman (arXiv:2012.04615). We then describe various properties of the automorphism S, showing that it is self-adjoint with respect to a certain non-degenerate symmetric bilinear form defined in terms of p-adic integration, and showing that its inverse plays a role in a p-adic integral-transform space akin to the role of differentiation in the classical space of Laplace-transformed functions. We also derive an integral-transform formula for the p-adic incomplete Γ-functions.