The Piltz divisor Problem in Number Fields Using The Resonance Method

2025/06/27 by Nilmoni Karak, Kamalakshya Mahatab, Karak, Nilmoni +1
Mathematics · Computer Science · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic

paper · pdf · doi:10.48550/arxiv.2506.22587

Abstract

The Piltz divisor problem is a natural generalization of the classical Dirichlet divisor problem. In this paper, we study this problem over number fields and obtain improved Ω-bounds for its error terms. Our approach involves generalizing a Voronoi-type formula due to Soundararajan in the number field setting, and applying a recent result due to the second author.

Citations

• Omega Results for The Divisor and Circle Problems Using The Resonance Method
• An improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem
• Extreme values of the Riemann zeta function on the 1-line
• Omega results for the divisor and circle problems

Related

• Piltz divisor problem over number fields à la Voronoï
• Omega Results for The Divisor and Circle Problems Using The Resonance Method
• Sign changes of the error term in the Piltz divisor problem
• On the number of integral ideals of a number field
• On a certain divisor function in Number fields