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


Authors: Sheng-Chi Liu and Riad Masri
Journal: Proc. Amer. Math. Soc. 143 (2015), 4143-4160
MSC (2010): Primary 11M41
DOI: https://doi.org/10.1090/proc/12495
Published electronically: June 5, 2015
MathSciNet review: 3373915
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Abstract: We establish a uniform asymptotic formula with a power saving error term for the average of the divisor function $ \tau (n):=\sum _{k\vert n}1$ over values of the quadratic polynomial $ x^2 +\vert D\vert$ where $ D < 0$ is a fundamental discriminant.


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Additional Information

Sheng-Chi Liu
Affiliation: Department of Mathematics, Washington State University, Pullman, Washington 99164-3113
Email: scliu@math.wsu.edu

Riad Masri
Affiliation: Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, Texas 77843-3368
Email: masri@math.tamu.edu

DOI: https://doi.org/10.1090/proc/12495
Received by editor(s): October 16, 2013
Received by editor(s) in revised form: March 3, 2014
Published electronically: June 5, 2015
Communicated by: Ken Ono
Article copyright: © Copyright 2015 American Mathematical Society

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