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1
Content available remote Kloosterman sums in residue rings
100%
Bourgain J. , Garaev M.
Acta Arithmetica
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2014
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tom 164
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nr 1
43-64
EN
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 ∈ 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.
2
Content available remote The Dunford-Pettis property for the ball-algebras, the polydisc-algebras and the Sobolev spaces
80%
Bourgain J.
Studia Mathematica
|
1983-1984
|
tom 77
|
nr 3
246-253
3
Content available A remark on gradients of harmonic functions in dimension ≥3
70%
Bourgain J. , Wolff T.
|
1990
|
tom 60-61
|
nr 1
253-260
4
Content available remote A stabilization property and its applications in theory of sections
70%
Bourgain J.
Fundamenta Mathematicae
|
1981
|
tom 112
|
nr 1
25-44
5
Content available remote A result on the isomorphic embeddability of l¹(Γ)
60%
Argyros S. , Bourgain J. , Zachariades T.
Studia Mathematica
|
1984
|
tom 78
|
nr 1
77-91
6
Content available remote Sets with the Radon-Nikodým property in conjugate Banach space
50%
Bourgain J.
|
1979-1980
|
tom 66
|
nr 3
291-297
7
Content available remote A direct proof of van der Vaart's theorem
41%
Bourgain J. , Sato H.
Studia Mathematica
|
1986
|
tom 84
|
nr 2
125-131
8
Content available remote A nondentable set without the tree property
40%
Bourgain J.
|
|
tom 68
|
nr 2
131-139
9
Content available remote Translation invariant complemented subspaces of $L^{p}$
40%
Bourgain J.
Studia Mathematica
|
1982-1983
|
tom 75
|
nr 1
95-101
10
Content available remote Borel sets with $F_σδ$-section
40%
Bourgain J.
Fundamenta Mathematicae
|
1980
|
tom 107
|
nr 2
149-159
11
Content available remote $F_σδ$-section of Borel sets
40%
Bourgain J.
Fundamenta Mathematicae
|
1980
|
tom 107
|
nr 2
129-133
12
Content available remote Dentability and finite-dimensional decompositions
40%
Bourgain J.
|
|
tom 67
|
nr 2
135-148
13
Content available remote A remark on finite-dimensional $P_{λ}$-spaces
40%
Bourgain J.
|
|
nr 3
285-289
14
Content available remote Sur le minimum d'une somme de cosinus
40%
Bourgain J.
|
|
nr 4
381-389
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