Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals

T. D. Browning; A. Haynes

doi:10.1142/S1793042112501448

Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals

T. D. Browning^*
, A. Haynes

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

Abstract

We investigate the solubility of the congruence xy equivalent to 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.

Original language	English
Pages (from-to)	481-486
Number of pages	6
Journal	International Journal of Number Theory
Volume	9
Issue number	2
DOIs	https://doi.org/10.1142/S1793042112501448
Publication status	Published - Mar 2013

Keywords

Incomplete Kloosterman sums
modular hyperbolas
Weil's bound

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Career Acceleration Fellowship
Haynes, A. K. (Principal Investigator)
1/10/11 → 1/10/13
Project: Research
DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY
Browning, T. D. (Principal Investigator)
1/09/07 → 1/04/13
Project: Research

Cite this

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title = "Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals",

abstract = "We investigate the solubility of the congruence xy equivalent to 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.",

keywords = "Incomplete Kloosterman sums, modular hyperbolas, Weil's bound",

author = "Browning, \{T. D.\} and A. Haynes",

year = "2013",

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language = "English",

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pages = "481--486",

journal = "International Journal of Number Theory",

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AU - Browning, T. D.

AU - Haynes, A.

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N2 - We investigate the solubility of the congruence xy equivalent to 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.

AB - We investigate the solubility of the congruence xy equivalent to 1 (mod p), where p is a prime and x, y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem for incomplete Kloosterman sums.

KW - Incomplete Kloosterman sums

KW - modular hyperbolas

KW - Weil's bound

U2 - 10.1142/S1793042112501448

DO - 10.1142/S1793042112501448

M3 - Article (Academic Journal)

SN - 1793-0421

VL - 9

SP - 481

EP - 486

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 2

ER -

Incomplete Kloosterman Sums and Multiplicative Inverses in Short Intervals

Abstract

Keywords

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Projects

Career Acceleration Fellowship

DIOPHANTINE GEOMETRY VIA ANALYTIC NUMBER THEORY

Cite this