TY - JOUR
T1 - Character sums with subsequence sums
AU - Balasuriya, Sanka
AU - Shparlinski, Igor E.
PY - 2007/11
Y1 - 2007/11
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=38049056827&partnerID=8YFLogxK
U2 - 10.1007/s10998-007-4215-4
DO - 10.1007/s10998-007-4215-4
M3 - Article
AN - SCOPUS:38049056827
SN - 0031-5303
VL - 55
SP - 215
EP - 221
JO - Periodica Mathematica Hungarica
JF - Periodica Mathematica Hungarica
IS - 2
ER -