A short note on the Pell-Lucas-Eisenstein series

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Uysal M., Inam I., Özkan E.

Asian-European Journal of Mathematics, vol.15, no.5, 2022 (ESCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1142/s1793557122502199
  • Journal Name: Asian-European Journal of Mathematics
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Eisenstein series, Pell-Lucas numbers, modular forms, integer partitions
  • Marmara University Affiliated: No

Abstract

© 2022 World Scientific Publishing Company.In this work, we define a new type of Eisenstein-like series by using Pell-Lucas numbers and call them the Pell-Lucas-Eisenstein Series. First, we show that the Pell-Lucas-Eisenstein series are convergent on their domain. Afterwards we prove that they satisfy some certain functional equations. Proofs follows from some on calculations on Pell-Lucas numbers.