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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The mean square discrepancy in the divisor problem


Authors: Fan Ge and Steven M. Gonek
Journal: Trans. Amer. Math. Soc. 373 (2020), 4713-4734
MSC (2010): Primary 11N37, 11N56
DOI: https://doi.org/10.1090/tran/8087
Published electronically: March 27, 2020
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Abstract: We study the mean square of the error term, or the mean square discrepancy, in the Dirichlet divisor problem. An analysis of the off-diagonal terms in the mean square of the Voronoi summation formula leads to a precise conjecture for this mean square discrepancy. Surprisingly, the discrepancy contains a slowly oscillating, unbounded term.


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Additional Information

Fan Ge
Affiliation: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23185
Email: fange.math@gmail.com

Steven M. Gonek
Affiliation: Department of Mathematics, University of Rochester, Rochester, New York 14627
Email: gonek@math.rochester.edu

DOI: https://doi.org/10.1090/tran/8087
Keywords: Dirichlet divisor problem, discrepancy estimates
Received by editor(s): December 7, 2017
Received by editor(s) in revised form: September 18, 2019
Published electronically: March 27, 2020
Additional Notes: The work of the second author was partially supported by NSF grant DMS-1200582.
Article copyright: © Copyright 2020 American Mathematical Society