A short note on the Pell-Lucas-Eisenstein series

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Uysal M., Inam I., Özkan E.

Asian-European Journal of Mathematics, cilt.15, sa.5, 2022 (ESCI) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 5
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1142/s1793557122502199
  • Dergi Adı: Asian-European Journal of Mathematics
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: Eisenstein series, Pell-Lucas numbers, modular forms, integer partitions
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

© 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.