Analytic expressions for some Mellin transforms with their application to prime counting function and interpolation formulas for the zeta function

2022/02/26 by Omprakash Atale, Atale, Omprakash
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2203.02278

openalex publication_date 2022/02/26 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

The aim of our present work here is to present few results in the theory of Mellin transforms using the method that S. Ramanujan used in proving his Master Theorem. Further applications of our results for some number-theoretic functions such as the prime counting function and the zeta function are established.

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