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Transactions of the American Mathematical Society

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

   
 
 

 

Counting integer points on quadrics with arithmetic weights


Author: V. Vinay Kumaraswamy
Journal: Trans. Amer. Math. Soc. 373 (2020), 6929-6959
MSC (2010): Primary 11F30, 11P55; Secondary 11E20
DOI: https://doi.org/10.1090/tran/8154
Published electronically: August 6, 2020
MathSciNet review: 4155196
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Abstract: Let $F \in \mathbf {Z}[\boldsymbol {x}]$ be a diagonal, non-singular quadratic form in four variables. Let $\lambda (n)$ be the normalised Fourier coefficients of a holomorphic Hecke form of full level. We give an upper bound for the problem of counting integer zeros of $F$ with $|\boldsymbol {x}| \leqslant X$, weighted by $\lambda (x_1)$.


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Additional Information

V. Vinay Kumaraswamy
Affiliation: School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom
MR Author ID: 1288484
Email: vinay.visw@gmail.com

Received by editor(s): February 2, 2018
Received by editor(s) in revised form: June 2, 2019, and October 11, 2019
Published electronically: August 6, 2020
Additional Notes: Part of this work was done while the author was a Program Associate in the Analytic Number Theory Program at the Mathematical Sciences Research Institute, Berkeley, USA, during Spring Semester 2017, which was supported by the National Science Foundation under grant no. DMS-1440140.
Article copyright: © Copyright 2020 by V. Vinay Kumaraswamy