A Brun-Titchmarsh inequality for weighted sums over prime numbers

TL;DR

This paper extends the Brun-Titchmarsh inequality to provide explicit upper bounds for weighted sums over primes in arithmetic progressions with slowly varying weights, enhancing understanding of prime distribution.

Contribution

It introduces a generalized Brun-Titchmarsh inequality applicable to weighted sums with slowly varying functions, offering explicit bounds.

Findings

Derived explicit upper bounds for weighted prime sums.

Generalized Brun-Titchmarsh inequality for new contexts.

Enhanced tools for studying primes in arithmetic progressions.

Abstract

We prove explicit upper bounds for weighted sums over prime numbers in arithmetic progressions with slowly varying weight functions. The results generalize the well-known Brun-Titchmarsh inequality.