An Explicit Formula For The Divisor Function

Abstract

The details for the construction of an explicit formula for the divisors function d(n) = #{d | n} are formalized in this article. This formula facilitates a unified approach to the investigation of the error terms of the divisor problem and circle problem.

arXiv commentTwenty Eight Pages. Keywords: Divisor Function, Explicit Formula, Divisor Problem

References in corpus (8)

• On sums of Fourier coefficients of cusp forms
• Sharp Bounds for the Harmonic Numbers
• The average number of solutions of the Diophantine equation U^2 + V^2 = W^3 and related arithmetic functions
• Some Problems in Number Theory I: The Circle Problem
• On the Riemann zeta-function and the divisor problem III
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• Primitive lattice points inside an ellipse

Cited by in corpus (1)

• Exact Formulas for the Generalized Sum-of-Divisors Functions