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Congruences Among Power Series Coefficients of Modular Forms

Number Theory 2013-10-09 v3

Abstract

Many authors have investigated the congruence relations amongst the coefficients of power series expansions of modular forms ff in modular functions tt. In a recent paper, R. Osburn and B. Sahu examine several power series expansions and prove that the coefficients exhibit congruence relations similar to the congruences satisfied by the Ap\'ery numbers associated with the irrationality of ζ(3)\zeta(3). We show that many of the examples of Osburn and Sahu are members of infinite families.

Keywords

Cite

@article{arxiv.1309.4320,
  title  = {Congruences Among Power Series Coefficients of Modular Forms},
  author = {Richard Moy},
  journal= {arXiv preprint arXiv:1309.4320},
  year   = {2013}
}

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24 pages