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On the average number of divisors of reducible quadratic polynomials. (arXiv:1704.06453v1 [math.NT])
来源于:arXiv
We give an asymptotic formula for the divisor sum $\sum_{c<n\leq
N}\tau\left((n-b)(n-c)\right)$ for integers $b<c$ of the same parity.
Interestingly, the coefficient of the main term does not depend on the
discriminant as long as it is a full square. We also provide effective upper
bounds of the average divisor sum for some of the reducible quadratic
polynomials considered before, with the same main term as in the asymptotic
formula. 查看全文>>