Heilbronn-like sums and their properties

H. Saydi and M. R. Darafsheh
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 104—112
DOI: 10.7546/nntdm.2021.27.3.104-112
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Authors and affiliations

H. Saydi
College of Mathematical Science, Tarbiat Modares University
Tehran, Iran

M. R. Darafsheh
School of Mathematics, Statistics and Computer Science
College of Science, University of Tehran, Tehran, Iran

Abstract

Heilbronn sums is of the form H_p(a)=\underset{l=1}{\overset{p-1}{\sum}}e(\dfrac{al^p}{p^2}), where p is an odd prime, and e(x)=\exp(2\pi ix). This is a supercharacter and has application in number theory. We extend this sum by defining D_p(a)=\underset{l=1}{\overset{p-1}{\sum}}e(\dfrac{al^p}{p^3}), where p is an odd prime and prove that D_p(a) is a supercharacter and drive a few identities involving D_p(a).

Keywords

  • Supercharacter
  • Heilbronn sum
  • Supercharacter table

2020 Mathematics Subject Classification

  • 20C15
  • 11T23

References

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Cite this paper

Saydi, H., & Darafsheh, M. R. (2021). Heilbronn-like sums and their properties. Notes on Number Theory and Discrete Mathematics, 27(3), 104-112, doi: 10.7546/nntdm.2021.27.3.104-112.

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