A Short Note on the Pell-Lucas-Eisenstein Series

Published 14 Jul 2022 in math.NT | (2207.06762v1)

Abstract: 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. Firstly, 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.

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