On the Pell-Einstein series of power m
Keywords:Eisenstein series, Pell numbers, modular forms, integer partitions
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.