The divisor function in arithmetic progressions to smooth moduli

2014/03/31 by A. J. Irving, Irving, A. J. · 4 citations
Mathematics · #Analytic Number Theory Research #Advanced Mathematical Identities #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1403.8031

Abstract

By using the q-analogue of van der Corput's method we study the divisor function in an arithmetic progression to modulus q. We show that the expected asymptotic formula holds for a larger range of q than was previously known, provided that q has a certain factorisation.

Cited by

• Primes in simultaneous arithmetic progressions
• On the exponent of distribution for convolutions of GL(2) coefficients to smooth moduli
• The divisor function along arithmetic progressions and binary cubic polynomials
• A new result on the divisor problem in arithmetic progressions modulo a prime power

Related

• Divisor problem in arithmetic progressions modulo a prime power
• A new result on the divisor problem in arithmetic progressions modulo a prime power
• Variance of the k-fold divisor function in arithmetic progressions for individual modulus
• The divisor function along arithmetic progressions and binary cubic polynomials
• Smooth numbers in arithmetic progressions to large moduli