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.

Twenty Eight Pages. Keywords: Divisor Function, Explicit Formula, Divisor Problem

References in corpus (5)

• On sums of Fourier coefficients of cusp forms
• The average number of solutions of the Diophantine equation U^2 + V^2 = W^3 and related arithmetic functions
• On the Riemann zeta-function and the divisor problem III
• Averages of shifted convolutions of $d_3(n)$
• Primitive lattice points inside an ellipse