Now showing 1 - 4 of 4
  • Publication
    A supercongruence for generalized Domb numbers
    (Faculty of Mathematics and Computer Science, Adam Mickiewicz University, 2013) ;
    Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one of Zagier's seven 'sporadic' solutions to second order Apery-like differential equations.
      235Scopus© Citations 11
  • Publication
    Supercongruences for sporadic sequences
    (Cambridge University Press, 2016-05) ; ;
    We prove two-term supercongruences for generalizations of recently discovered sporadic sequences of Cooper. We also discuss recent progress and future directions concerning other types of supercongruences.
    Scopus© Citations 24  426
  • Publication
    Supercongruences for Apéry-like numbers
    (Elsevier, 2011-09) ;
    It is known that the numbers which occur in Apery's proof of the irrationality of zeta (2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukers' and Zagier's study of integral solutions of Apery-like differential equations.
      330Scopus© Citations 14
  • Publication
    Congruences via modular forms
    (American Mathematical Society, 2011) ;
    We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide tables of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apery-like differential equations.
      239Scopus© Citations 8