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On the concentration of points on modular hyperbolas and exponential curves
被引:14
作者
:
Chan, Tsz Ho
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
Chan, Tsz Ho
[
1
]
Shparlinski, Igor E.
论文数:
0
引用数:
0
h-index:
0
机构:
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
Shparlinski, Igor E.
[
2
]
机构
:
[1]
Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
[2]
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
来源
:
ACTA ARITHMETICA
|
2010年
/ 142卷
/ 01期
关键词
:
modular hyperbola;
modular exponential curve;
sum-product estimates;
concentration function;
SUM-PRODUCT ESTIMATE;
D O I
:
10.4064/aa142-1-5
中图分类号
:
O1 [数学];
学科分类号
:
0701 ;
070101 ;
摘要
:
[No abstract available]
引用
收藏
页码:59 / 66
页数:8
相关论文
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A sum-product estimate in finite fields, and applications
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Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
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GEOMETRIC AND FUNCTIONAL ANALYSIS,
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Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm
[J].
Bourgain, Jean
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Inst Adv Study, Princeton, NJ 08540 USA
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
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Konyagin, Sergei V.
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0
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Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119992, Russia
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
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Shparlinski, Igor E.
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Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
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.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES,
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2008
[4]
Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings and Fixed Points of the Discrete Logarithm (vol 1, pg 29, 2008)
[J].
Bourgain, Jean
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Inst Adv Study Princeton, Princeton, NJ 08540 USA
Inst Adv Study Princeton, Princeton, NJ 08540 USA
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Konyagin, Sergei V.
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h-index:
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VA Steklov Math Inst, Moscow 119991, Russia
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.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES,
2009,
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(16)
:3146
-3147
[5]
On the smallest pseudopower
[J].
Bourgain, Jean
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0
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Inst Adv Study, Princeton, NJ 08540 USA
Inst Adv Study, Princeton, NJ 08540 USA
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Konyagin, Sergei V.
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On a variant of sum-product estimates and explicit exponential sum bounds in prime fields
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:2735
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On the logarithmic factor in error term estimates in certain additive congruence problems
[J].
Garaev, M. Z.
论文数:
0
引用数:
0
h-index:
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机构:
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Garaev, M. Z.
.
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←
1
2
→
共 18 条
[1]
A sum-product estimate in finite fields, and applications
[J].
Bourgain, J
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
Bourgain, J
;
Katz, N
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
Katz, N
;
Tao, T
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study, Sch Math, Princeton, NJ 08540 USA
Tao, T
.
GEOMETRIC AND FUNCTIONAL ANALYSIS,
2004,
14
(01)
:27
-57
[2]
BOURGAIN J, 2008, DIVISIBILITY FERMAT
[3]
Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings, and Fixed Points of the Discrete Logarithm
[J].
Bourgain, Jean
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study, Princeton, NJ 08540 USA
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Bourgain, Jean
;
Konyagin, Sergei V.
论文数:
0
引用数:
0
h-index:
0
机构:
Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119992, Russia
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Konyagin, Sergei V.
;
Shparlinski, Igor E.
论文数:
0
引用数:
0
h-index:
0
机构:
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Shparlinski, Igor E.
.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES,
2008,
2008
[4]
Product Sets of Rationals, Multiplicative Translates of Subgroups in Residue Rings and Fixed Points of the Discrete Logarithm (vol 1, pg 29, 2008)
[J].
Bourgain, Jean
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study Princeton, Princeton, NJ 08540 USA
Inst Adv Study Princeton, Princeton, NJ 08540 USA
Bourgain, Jean
;
Konyagin, Sergei V.
论文数:
0
引用数:
0
h-index:
0
机构:
VA Steklov Math Inst, Moscow 119991, Russia
Inst Adv Study Princeton, Princeton, NJ 08540 USA
Konyagin, Sergei V.
;
Shparlinski, Igor E.
论文数:
0
引用数:
0
h-index:
0
机构:
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Inst Adv Study Princeton, Princeton, NJ 08540 USA
Shparlinski, Igor E.
.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES,
2009,
2009
(16)
:3146
-3147
[5]
On the smallest pseudopower
[J].
Bourgain, Jean
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study, Princeton, NJ 08540 USA
Inst Adv Study, Princeton, NJ 08540 USA
Bourgain, Jean
;
Konyagin, Sergei V.
论文数:
0
引用数:
0
h-index:
0
机构:
Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow 119992, Russia
Inst Adv Study, Princeton, NJ 08540 USA
Konyagin, Sergei V.
;
Pomerance, Carl
论文数:
0
引用数:
0
h-index:
0
机构:
Dartmouth Coll, Dept Math, Hanover, NH 03755 USA
Inst Adv Study, Princeton, NJ 08540 USA
Pomerance, Carl
;
Shparlinski, Igor E.
论文数:
0
引用数:
0
h-index:
0
机构:
Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
Inst Adv Study, Princeton, NJ 08540 USA
Shparlinski, Igor E.
.
ACTA ARITHMETICA,
2009,
140
(01)
:43
-55
[6]
On a variant of sum-product estimates and explicit exponential sum bounds in prime fields
[J].
Bourgain, L.
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Adv Study, Princeton, NJ 08540 USA
Inst Adv Study, Princeton, NJ 08540 USA
Bourgain, L.
;
Garaev, M. Z.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Inst Adv Study, Princeton, NJ 08540 USA
Garaev, M. Z.
.
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY,
2009,
146
:1
-21
[7]
PLoS computational biology:: A new community journal
[J].
Bourne, PE
论文数:
0
引用数:
0
h-index:
0
Bourne, PE
;
Brenner, SE
论文数:
0
引用数:
0
h-index:
0
Brenner, SE
;
Eisen, MB
论文数:
0
引用数:
0
h-index:
0
Eisen, MB
.
PLOS COMPUTATIONAL BIOLOGY,
2005,
1
(01)
:1
-1
[8]
Chan T. H., 2004, INTEGERS, V4
[9]
The sum-product estimate for large subsets of prime fields
[J].
Garaev, M. Z.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Garaev, M. Z.
.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,
2008,
136
(08)
:2735
-2739
[10]
On the logarithmic factor in error term estimates in certain additive congruence problems
[J].
Garaev, M. Z.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Univ Nacl Autonoma Mexico, Inst Matemat, Morelia 58089, Michoacan, Mexico
Garaev, M. Z.
.
ACTA ARITHMETICA,
2006,
124
(01)
:27
-39
←
1
2
→