Jean Bourgain

most citedSumsets of reciprocals in prime fields and multilinear Kloosterman sums

11 citations · 12 across the 3 of their papers we have counts for

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math.NT2013★ 1 cited

Kloosterman sums in residue rings

J. Bourgain, M. Z. Garaev

In the present paper, we generalize some of the results on Kloosterman sums proven in \cite{BG} for prime moduli to general moduli. This requires to establish the corresponding add…

math.NT2012★ 11 cited

Sumsets of reciprocals in prime fields and multilinear Kloosterman sums

J. Bourgain, M. Z. Garaev

We obtain new results on additive properties of the set $I^{- 1} = {x^{- 1} : x \in I}$ where $I$ is an arbitrary interval in the field of residue classes modulo a large pri…

math.NT2012

Multiplicative Congruences with Variables from Short Intervals

Jean Bourgain, Moubariz Z. Garaev, Sergei V. Konyagin +1

Recently, several bounds have been obtained on the number of solutions to congruences of the type $(x_{1} + s) ... (x_{ν} + s) \equiv (y_{1} + s) ... (y_{ν} + s) \neq \equiv 0 (mod p)$ modulo a prime…