Eisenstein Series

Xueli Wang () and Dingyi Pei ()
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Xueli Wang: South China Normal University, Department of Mathematics
Dingyi Pei: Guangzhou University, Institute of Mathematics and Information Science

Chapter Chapter 2 in Modular Forms with Integral and Half-Integral Weights, 2012, pp 13-43 from Springer

Abstract: Abstract In this section we always assume that k is an odd integer, N is a positive integer such that 4|N, ω is an even character modulo N, i.e., ω(−1) = 1. We shall construct a class of holomorphic functions which are named as Eisenstein series with the following property $$ f\left( {\gamma \left( z \right)} \right) = \omega (d_\gamma )j(\gamma ,z)^k f(z),\quad \gamma = \left( {\begin{array}{*{20}c} * & * \\ * & {d_\gamma } \\ \end{array} } \right)\; \in \Gamma _0 (N). $$

Date: 2012
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DOI: 10.1007/978-3-642-29302-3_2

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