Character sums with subsequence sums

Sanka Balasuriya; Igor E. Shparlinski

doi:10.1007/s10998-007-4215-4

Character sums with subsequence sums

Sanka Balasuriya^*, Igor E. Shparlinski

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 T_m S χ = ∑ _I 1... ,N χ ∑ _i I {s_i taken over all N-element sequences S = (s ₁,...,s_N) 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 language	English
Pages (from-to)	215-221
Number of pages	7
Journal	Periodica Mathematica Hungarica
Volume	55
Issue number	2
DOIs	https://doi.org/10.1007/s10998-007-4215-4
Publication status	Published - Nov 2007

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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.",

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AB - 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.

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Character sums with subsequence sums

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