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Ling Long

  1. Hypergeometric evaluation identities and supercongruences.

    Ср, 12/02/2009 - 16:01 — SomNambul
    Authors: Ling Long
    Subjects: Number Theory
    Abstract

    In this article, we provide a delightful application of hypergeometric
    evaluation identities, including a strange valuation of Gosper, to prove
    several supercongruences related to special valuations of truncated
    hypergeometric series. Among them is the following conjecture of van Hamme: for
    any prime $p>3$, $\sum_{k=0}^{(p-1)/2} (6k+1) ((1/2)_k / k!)^3 4^{-k} \equiv
    (-1)^{(p-1)/2}p \mod p^4$.

  2. Zeros of some level 2 Eisenstein series.

    Ср, 08/26/2009 - 14:58 — SomNambul
    Authors: Sharon Garthwaite, Ling Long, Holly Swisher, Stephanie Treneer
    Subjects: Number Theory
    Abstract

    The zeros of classical Eisenstein series satisfy many intriguing properties.
    Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc
    of the fundamental domain, and recent work by Nozaki explores their interlacing
    property. In this paper we extend these distribution properties to a particular
    family of Eisenstein series on Gamma(2) because of its elegant connection to a
    classical Jacobi elliptic function cn(u) which satisfies a differential
    equation.

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