On Linnik's Conjecture: Sums of Squares and Microsquares

Trevor D. Wooley*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

Abstract

We show that almost all natural numbers n not divisible by 4, and not congruent to 7 modulo 8, are represented as the sum of three squares, one of which is the square of an integer no larger than (log n)(1+epsilon). This answers a conjecture of Linnik for almost all natural numbers, and sharpens a conclusion of Bourgain, Rudnick, and Sarnak concerning nearest neighbor distances between normalized integral points on the sphere.

Original languageEnglish
Pages (from-to)5713-5736
Number of pages24
JournalInternational Mathematics Research Notices
Issue number20
DOIs
Publication statusPublished - 2014

Keywords

  • HALF-INTEGRAL WEIGHT
  • FORMS

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