Periodica Mathematica Hungarica
Volume/Issue:
Volume 55: Issue 2
Character sums with subsequence sums
Authors:
Sanka Balasuriya Macquarie University Department of Computing Sydney NSW 2109 Australia

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Igor Shparlinski Macquarie University Department of Computing Sydney NSW 2109 Australia

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Pages:
215–221
Online Publication Date:
08 Jan 2008
Publication Date:
01 Nov 2007
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10998-007-4215-4
Keywords:
11B50; 11L40; subsequence sums; character sums; squares
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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
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$T_m (\mathcal{S},\chi ) = \sum\nolimits_{\mathcal{I} \subseteq \{ 1, \ldots ,N\} } {\chi (\sum\nolimits_{i \in \mathcal{I}} {s_i } )}$$ \end{document}
taken over all N-element sequences S = (s1, …, sN) of integer elements in a given interval [K + 1, K + L]. In particular, we show that Tm(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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Cover Periodica Mathematica Hungarica
Periodica Mathematica Hungarica
Print ISSN:
0031-5303
Online ISSN:
1588-2829

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1971
Volumes
per Year		 2
Issues
per Year		 4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address		 H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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