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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Upper bounds for the number of solutions of a Diophantine equation


Author: M. Z. Garaev
Journal: Trans. Amer. Math. Soc. 357 (2005), 2527-2534
MSC (2000): Primary 11D45, 11L03
Published electronically: December 28, 2004
MathSciNet review: 2140449
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Abstract: We give upper bound estimates for the number of solutions of a certain diophantine equation. Our results can be applied to obtain new lower bound estimates for the $L_1$-norm of certain exponential sums.


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Additional Information

M. Z. Garaev
Affiliation: Instituto de Matemáticas UNAM, Campus Morelia, Ap. Postal 61-3 (Xangari) CP 58089, Morelia, Michoacán, México
Email: garaev@matmor.unam.mx

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03611-6
PII: S 0002-9947(04)03611-6
Keywords: Diophantine equation, Karatsuba's theorem, Konyagin's estimate
Received by editor(s): September 8, 2003
Received by editor(s) in revised form: January 10, 2004
Published electronically: December 28, 2004
Article copyright: © Copyright 2004 American Mathematical Society