When is the derivative of an eta quotient another eta quotient?

[摘要] In this paper we use techniques from the theory of modular forms to determine all eta quotients whose derivative is also an eta quotient of levels up to 36. In addition, we present an algorithm that determines all eta quotients in M-2k(Gamma(0)(N)). We also discuss some applications of these results. In particular, we evaluate a number of integrals in terms of algebraic constants. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Eisenstein series;Dedekind eta function;Eta quotients;Modular forms;Derivatives;Algorithms