A Bombieri-type theorem for convolution with application on number field

Authors

P. Darbar, Indian Statistical Institute, Kolkata
A. Mukhopadhyay, Institute of Mathematical Sciences India

Article Type

Research Article

Publication Title

Acta Mathematica Hungarica

Abstract

Let K be an imaginary quadratic number field and OK be itsring of integers. We show that, if the arithmetic functions f, g: OK→ C both havelevel of distribution ϑ for some 0 < ϑ≤ 1 / 2 then the Dirichlet convolution f∗ galso has level of distribution ϑ. As an application we also obtain an analogue ofthe Titchmarsh divisor problem for product of two primes in imaginary quadraticfields.

First Page

37

Last Page

61

DOI

10.1007/s10474-020-01104-8

Publication Date

2-1-2021

Recommended Citation

Darbar, P. and Mukhopadhyay, A., "A Bombieri-type theorem for convolution with application on number field" (2021). Journal Articles. 2106.
https://digitalcommons.isical.ac.in/journal-articles/2106