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Upper bounds for the number of solutions of a Diophantine equation

Author(s): M. Z. Garaev
Journal: Trans. Amer. Math. Soc. 357 (2005), 2527-2534.
MSC (2000): Primary 11D45, 11L03
Posted: December 28, 2004
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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: 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
Posted: December 28, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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