The average of the divisor function over values of a quadratic polynomial

Liu, Sheng-Chi; Masri, Riad

doi:10.1090/proc/12495

The average of the divisor function over values of a quadratic polynomial
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by Sheng-Chi Liu and Riad Masri PDF

Proc. Amer. Math. Soc. 143 (2015), 4143-4160 Request permission

Abstract:

We establish a uniform asymptotic formula with a power saving error term for the average of the divisor function $\tau (n):=\sum _{k|n}1$ over values of the quadratic polynomial $x^2 +|D|$ where $D < 0$ is a fundamental discriminant.

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