Character sums with subsequence sums

Sanka Balasuriya*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let χ be a primitive multiplicative character modulo an integer m ≥ 1. Using some classical bounds of character sums, we estimate the average value of the character sums with subsequence sums Tm S χ = ∑ I 1... ,N χ ∑ i I {si taken over all N-element sequences S = (s 1,...,sN) of integer elements in a given interval [K + 1, K + L]. In particular, we show that T m (S, χ) is small on average over all such sequences. We apply it to estimating the number of perfect squares in subsequence sums in almost all sequences.

Original languageEnglish
Pages (from-to)215-221
Number of pages7
JournalPeriodica Mathematica Hungarica
Volume55
Issue number2
DOIs
Publication statusPublished - Nov 2007

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