Multiples of squares in short intervals

Joël Rivat, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review


We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form [x; x+x1=2] contains an integral multiple m2r ∈ [x; x+x1=2] of a perfect square m2 with an integer m > x0:281286.

Original languageEnglish
Pages (from-to)57-63
Number of pages7
JournalFunctiones et Approximatio, Commentarii Mathematici
Issue number1
Publication statusPublished - 2016
Externally publishedYes


  • Exponential sums
  • Multiples of squares
  • Short intervals


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