EQUIDISTRIBUTION OF DIVISORS IN RESIDUE CLASSES AND REPRESENTATIONS BY BINARY QUADRATIC FORMS

作者：Drmota Michael^*; Skalba Mariusz

来源：International Journal of Number Theory, 2013, 9(8): 2011-2018.

DOI：10.1142/S1793042113500711

• Divisors
• equidistribution
• Davenport constant
• binary quadratic forms

We study the number of divisors in residue classes modulo m and prove, for example, that the exact equidistribution holds for almost all natural numbers coprime to m in the sense of natural density if and only if m = 2(k)p(1)p(2) ... p(s), where k and s are non-negative integers and p(j) are distinct Fermat primes. We also provide a general and exact lower bound for the proportion of divisors in the residue class 1 mod m. The same combinatorial technique using Davenport%26apos;s constant leads to exact lower bounds for the number of representations of a natural number by a given binary quadratic form with a negative discriminant.

• 出版日期2013-12