# Fractional parts of polynomials over the primes. II

## TL;DR

This paper improves the understanding of how closely quadratic polynomials with irrational leading coefficients evaluated at prime numbers approximate integers, demonstrating that the fractional parts are very small for infinitely many primes.

## Contribution

It provides a 14% improvement in the exponent measuring the proximity of polynomial values to integers at prime arguments compared to previous results.

## Key findings

- Fractional parts of quadratic polynomials at primes are very small infinitely often.
- Achieved a 14% enhancement over previous bounds.
- Results contribute to understanding polynomial behavior over primes.

## Abstract

We consider the distance to the nearest integer of f(p), where f is a quadratic polynomial with irrational leading coefficient. This distance is very small as a function of p, for infinitely many primes p. We give a 14% improvement in the exponent that measures the distance, compared with the most recent result in the literature.