exp-pairs-0.2.1.0: Linear programming over exponent pairs

Math.ExpPairs.MenzerNowak

Description

Asymmetric divisor problem with congruence conditions

Let τ_{a, b}(l_1, k_1; l_2, k_2; n) denote the number of integer (v, w) with v^a w^b = n, v ≡ l_1 (mod k_1), w ≡ l_2 (mod k_2).

Menzer and Nowak (Menzer H., Nowak W. G. `On an asymmetric divisor problem with congruence conditions' // Manuscr. Math., 1989, Vol. 64, no. 1, P. 107-119) proved an asymptotic formula for Σ_{n ≤ x} τ_{a, b}(l_1, k_1; l_2, k_2; n) with an error term of order (x / k_1^a / k_2^b)^(Θ(a, b) + ε). They provided an expression for Θ(a, b) in terms of exponent pairs.

Synopsis

Documentation

Compute Θ(a, b) for given a and b.