On the constant terms of certain meromorphic modular forms for Hecke groups
Abstract
We study polynomials interpolating the (rational) constant terms of certain meromorphic modular forms for Hecke groups. We make observations about the divisibility properties of the constant terms and connect them to several sequences, for example, to O.E.I.S. sequence A005148 OEISNewmanShanks, which was studied by Newman, Shanks and Zagier newman2004sequence, newman2004sequenceAppendix in an article on its use in series approximations to π.
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