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  • Publication
    Sequences, modular forms and cellular integrals
    (Cambridge University Press, 2020-03) ; ;
    It is well-known that the Apéry sequences which arise in the irrationality proofs for ζ(2) and ζ(3) satisfy many intriguing arithmetic properties and are related to the pth Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.
      5Scopus© Citations 6
  • Publication
    A p-adic analogue of a formula of Ramanujan
    During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.
      431Scopus© Citations 54