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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Counting integer points on quadrics with arithmetic weights
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by V. Vinay Kumaraswamy PDF
Trans. Amer. Math. Soc. 373 (2020), 6929-6959

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.
  • © Copyright 2020 by 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
  • MathSciNet review: 4155196