# A generalization of Bombieri-Vinogradov theorem and its application

## TL;DR

This paper generalizes the Bombieri-Vinogradov theorem to primes represented by binary quadratic forms and applies it to extend results on bounded gaps between Gaussian primes.

## Contribution

It introduces a new generalized theorem for primes represented by quadratic forms and applies it to improve understanding of Gaussian prime gaps.

## Key findings

- Generalized Bombieri-Vinogradov theorem for quadratic form primes
- Extended bounded gap results to Gaussian primes
- Demonstrated applications to prime distribution in quadratic forms

## Abstract

In this paper we establish a generalization of Bombieri-Vinogradov theorem for primes represented by a fixed positive definite binary quadratic form. Then we apply this theorem to generalize a result of Vatwani on bounded gap between Gaussian primes.