Corpus ID: 119725351

O'Nan moonshine and arithmetic

  title={O'Nan moonshine and arithmetic},
  author={John F. R. Duncan and Michael H. Mertens and Ken Ono},
  journal={arXiv: Number Theory},
  • John F. R. Duncan, Michael H. Mertens, Ken Ono
  • Published 2017
  • Mathematics
  • arXiv: Number Theory
  • Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple group of O'Nan, for which the McKay--Thompson series are weight $3/2$ modular forms. The coefficients of these series may be expressed in terms of class numbers, traces of singular moduli, and central critical values of quadratic twists of weight 2 modular $L$-functions. As a consequence, for primes $p$ dividing the… CONTINUE READING

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