Abstract
Recently H. Farkas introduced a new simple arithmetic function and found an identity which involves this function. It is immediate to rewrite this identity as an identity between modular forms and reprove it in this way. We discuss natural generalizations of Farkas’ identity. Surprisingly, in a certain sense, there is only one identity which is an exact analogue of that found by Farkas. At the same time, we present a way to produce infinitely many similar identities. As an application, we obtain a result on non-vanishing of the central critical value of L-functions associated to a cusp Hecke eigenform.
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