2015/09/15 by Tomohiro Ikkai, Ikkai, Tomohiro
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.1509.04408
15 pages
arxiv created 2015/09/15 · openalex publication_date 2015/09/15 · arxiv updated 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Picking binomial coefficients which cannot be divided by a given prime from Pascal's triangle, we find that they form a set with self-similarity. Essouabri studied on a class of meromorphic functions associated to the above set. These functions are related to fractal geometry and it is a problem whether such a function has a non-real pole on its axis of absolute convergence. Essouabri gave a proof of existence of such a non-real pole in the simplest case. The keys of his proof are Stein's and Wilson's estimates on how fast the points multiply in Pascal's triangle modulo a prime. This article will give an extension of Essouabri's result to some cases with certain ways to count the points in Pascal's triangle modulo a prime which are different from the traditional one.