On the Pell-Einstein series of power m

Authors

  • I. Inam Bilecik Seyh Edebali University, Turkey
  • E. Ozkan Erzincan Binali Yildirim University, Turkey
  • M. Uysal Erzincan Binali Yildirim University, Turkey
  • Z.D. Ozkaya Van Yuzuncu Yil University, Turkey

DOI:

https://doi.org/10.31926/but.mif.2022.2.64.1.6

Keywords:

Eisenstein series, Pell numbers, modular forms, integer partitions

Abstract

In this paper, we introduce the Pell-Eisenstein Series which is obtained by Pell numbers and they are a new class of Eisenstein-type series. First, we see that they are well-defined and then we prove that the Pell-Eisenstein series satisfies some functional equations. Proofs are based on properties of Pell numbers and calculations.

Author Biographies

I. Inam, Bilecik Seyh Edebali University, Turkey

Faculty of Arts and Sciences, Department of Mathematics 11200

E. Ozkan, Erzincan Binali Yildirim University, Turkey

Faculty of Arts and Sciences, Department of Mathematics 24002

M. Uysal, Erzincan Binali Yildirim University, Turkey

Faculty of Arts and Sciences, Department of Mathematics 24002

Z.D. Ozkaya, Van Yuzuncu Yil University, Turkey

Muradiye Vocational School 65080

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Published

2022-07-06

Issue

Vol. 2(64) No. 1 (2022)

Section

MATHEMATICS