An analytic approach to the remainder terms in the asymptotic formulas -- the Volterra integral equation, the Whittaker function

2023/02/14 by Hideto Iwata, Iwata, Hideto · 1 citation
Mathematics · #Advanced Mathematical Identities #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.06779

openalex publication_date 2023/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, firstly, we consider the Volterra integral equation of second type for a remainder term in an asymptotic formula of an arithmetic function which satisfies some special conditions and obtained a solution of the equation. The method using there is applied to the remainder term in an asymptotic formula of the associated Euler totient function. Secondly, we consider a function defined a series over all non-trivial zeros of the generalized L-functions. We proved some analytic properties which satisfy some conditions. In particular, we use the Whittaker function which is kind of the confluent hypergeometric function there.

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• A relation to a remainder terms in an asymptotic formula for the associated Euler totient function

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