The Selberg-Delange method and mean value of arithmetic functions over short intervals
Amrinder Kaur, Ayyadurai Sankaranarayanan
TL;DR
This paper applies the Selberg-Delange method with the Hooley-Huxley contour to derive mean value results of arithmetic functions over shorter intervals, advancing understanding of their distribution in number theory.
Contribution
It introduces a novel application of the Selberg-Delange method combined with the Hooley-Huxley contour to analyze arithmetic functions over short intervals.
Findings
Established mean value results for arithmetic functions over shorter intervals.
Extended the applicability of the Selberg-Delange method in analytic number theory.
Provided new insights into the distribution of arithmetic functions in short segments.
Abstract
In this paper, we establish a mean value result of arithmetic functions over shorter intervals with the Selberg-Delange method using the Hooley-Huxley contour.
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Taxonomy
TopicsMeromorphic and Entire Functions · Functional Equations Stability Results · advanced mathematical theories