On the representation of integers by indefinite binary Hermitian forms

TL;DR

This paper provides an asymptotic formula for counting the number of integer representations by indefinite binary Hermitian forms over imaginary quadratic fields, considering congruence conditions as the bound grows.

Contribution

It offers a precise asymptotic equivalent for the count of integer representations by indefinite binary Hermitian forms over imaginary quadratic fields, including congruence restrictions.

Findings

Asymptotic equivalent for representation count derived

Includes congruence properties in the analysis

Applicable to integers with bounded absolute value

Abstract

Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.