Now showing 1 - 4 of 4
  • Publication
    Representations of integers by certain positive definite binary quadratic forms
    (Springer, 2007-12) ;
    We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x2+Ny2 for a squarefree integer N.
      216
  • Publication
    On sums of three squares
    (World Scientific Publishing, 2005-06) ; ;
    Let r3(n) be the number of representations of a positive integer n as a sum of three squares of integers. We give two distinct proofs of a conjecture of Wagon concerning the asymptotic value of the mean square of r3(n).
      199
  • Publication
    Congruences for Traces of Singular Moduli
    (Springer, 2007-12)
    We extend a result of Ahlgren and Ono [1] on congruences for traces of singular moduli of level 1 to traces defined in terms of Hauptmodul associated to certain groups of genus 0 of higher levels.
    Scopus© Citations 6  218
  • 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.
      234Scopus© Citations 8