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THE NUMBER OF SOLUTIONS TO MORDELL’S EQUATION IN CONSTRAINED RANGES

Part of: Additive number theory; partitions Exponential sums and character sums

Published online by Cambridge University Press:  05 December 2014

Matthew P. Young
Matthew P. Young*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, U.S.A. email myoung@math.tamu.edu
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Abstract

We estimate the number of solutions to $|y^{2}-x^{3}|\leqslant X$ with $N\leqslant y\leqslant 2N$, in terms of both $N$ and $X$.

MSC classification

Primary: 11L07: Estimates on exponential sums 11P21: Lattice points in specified regions
Type
Research Article
Information
Mathematika , Volume 61 , Issue 3 , September 2015 , pp. 708 - 718
Copyright
Copyright © University College London 2014 

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