On small solutions to quadratic congruences

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We estimate the deviation of the number of solutions of the congruence. m2-n2≡c(modq),1≤m≤M,1≤n≤N, from its expected value on average over c=1,...,q. This estimate is motivated by the connection, recently established by D.R. Heath-Brown, between the distribution of solution to this congruence and the pair correlation problem for the fractional parts of the quadratic function αk2, k=1,2,... with a real α.

Original languageEnglish
Pages (from-to)1105-1111
Number of pages7
JournalJournal of Number Theory
Volume131
Issue number6
DOIs
Publication statusPublished - Jun 2011

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