On Eisenstein series in M2k(Γ0(N)) and their applications

• Main Author: Aygin, Zafer Selcuk
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Sum of Divisors Function; Convolution Sums
• Online Access: https://hdl.handle.net/10356/143236
• Institution: Nanyang Technological University

Let k, N ∈ N with N square-free and k > 1. We prove an orthogonal relation and use this to compute the Fourier coefficients of the Eisenstein part of any f(z) ∈ M2k(Γ0(N)) in terms of sum of divisors function. In particular, if f(z) ∈ E2k(Γ0(N)), then the computation will to yield to an expressio...