Distribution of points on modular hyperbolas

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

We give a survey of several recent results and pose several open problems about the distribution and some geometric properties of points (x, y) on modular hyperbolas xy equivalent to a (mod m). We also outline a very diverse range of applications of such results and discuss multivariate generalisations.

Original languageEnglish
Title of host publicationProceedings of the 4th China-Japan Seminar on Number Theory
Subtitle of host publicationsailing on the sea of number theory
EditorsS. Kanemitsu, J.-Y. Liu
Place of PublicationSingapore
PublisherWorld Scientific Publishing
Pages155-189
Number of pages35
Volume2
ISBN (Print)9789812708106
DOIs
Publication statusPublished - 2007
Event4th China-Japan Seminar on Number Theory - Weihai, China
Duration: 30 Aug 20063 Sep 2006

Publication series

NameSeries on Number Theory and Its Applications
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
Volume2
ISSN (Print)1793-3161

Conference

Conference4th China-Japan Seminar on Number Theory
CountryChina
CityWeihai
Period30/08/063/09/06

Keywords

  • INVERSES MOD-Q
  • F-P-POINTS
  • D-H-LEHMER
  • KLOOSTERMAN SUMS
  • CHARACTER SUMS
  • RATIONAL FUNCTIONS
  • QUADRATIC RESIDUE
  • EXPONENTIAL-SUMS
  • DIVISOR PROBLEM
  • SHORT INTERVALS

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