1. On the Number of Divisors of the Quadratic Form m2 + n2
- Author
-
Gang Yu
- Subjects
Discrete mathematics ,Practical number ,General Mathematics ,010102 general mathematics ,Deficient number ,Divisor function ,010103 numerical & computational mathematics ,Divisor (algebraic geometry) ,Table of divisors ,01 natural sciences ,Semiperfect number ,Binary quadratic form ,Quadratic field ,0101 mathematics ,Mathematics - Abstract
For an integer n, let d(n) denote the ordinary divisor function. This paper studies the asymptotic behavior of the sumIt is proved in the paper that, as x → ∞,where A1 and A2 are certain constants and ε is any fixed positive real number.The result corrects a false formula given in a paper of Gafurov concerning the same problem, and improves the error claimed by Gafurov.
- Published
- 2000