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Note on a result of Shparlinski and related results

Volume 193 / 2020

Norbert Hegyvári, Máté Pálfy Acta Arithmetica 193 (2020), 157-163 MSC: Primary 11B30, 11L03; Secondary 11B75. DOI: 10.4064/aa181018-8-4 Published online: 16 January 2020

Abstract

Using graph spectra, we give a new proof of a statement of Shparlinski which was the main tool in the estimation of the energy of a distance set and we derive some consequence of it. Assuming some additional condition, we give a new estimation on the energy of the distance set.

Authors

  • Norbert HegyváriInstitute of Mathematics
    Eötvös University
    Pázmány St. 1/c
    H-1117 Budapest, Hungary
    e-mail
  • Máté PálfyInstitute of Mathematics
    Eötvös University
    Pázmány St. 1/c
    H-1117 Budapest, Hungary
    e-mail

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