Geodesic
Kloosterman sums in residue rings
J. Bourgain1 ; M. Z. Garaev2
1 Institute for Advanced Study Princeton, NJ 08540, U.S.A.
2 Centro de Ciencias Matemáticas Universidad Nacional Autónoma de México Morelia 58089, Michoacán, México
Acta Arithmetica, Tome 164 (2014) no. 1, pp. 43-64 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We generalize some of our previous results on Kloosterman sums [Izv. Mat., to appear] for prime moduli to general moduli. This requires establishing the corresponding additive properties of the reciprocal-set $ I^{-1}=\{x^{-1}: x\in I\}, $ where $I$ is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun–Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of general moduli.
DOI : 10.4064/aa164-1-4
Keywords: generalize previous results kloosterman sums izv mat appear prime moduli general moduli requires establishing corresponding additive properties reciprocal set where interval ring residue classes modulo large positive integer apply bounds multilinear exponential sums brun titchmarsh theorem estimate short kloosterman sums hence generalizing earlier work setting general moduli

J. Bourgain 1 ; M. Z. Garaev 2

1 Institute for Advanced Study Princeton, NJ 08540, U.S.A.
2 Centro de Ciencias Matemáticas Universidad Nacional Autónoma de México Morelia 58089, Michoacán, México 
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J. Bourgain; M. Z. Garaev. Kloosterman sums in residue rings. Acta Arithmetica, Tome 164 (2014) no. 1, pp. 43-64. doi: 10.4064/aa164-1-4

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