On Simplifications of Certain q-Multisums

The Bailey Chain and Mock Theta Functions

Standard applications of the Bailey chain preserve mixed mock modularity but not mock modularity. After illustrating this with some examples, we show how to use a change of base in Bailey pairs due to Bressoud, Ismail and Stanton to explicitly construct families of q-hypergeometric multisums which are mock theta functions. We also prove identities involving some of these multisums and certain c...

Product Representations in Πσ-fields

ΠΣ-fields are a very general class of difference fields that enable one to discover and prove multisum identities arising in combinatorics and special functions. In this article we focus on the problem how such multisums can be represented in terms of ΠΣ-fields. In particular we consider product representations and their simplifications in ΠΣ-fields.

Bailey Pairs and Indefinite Quadratic Forms

We construct classes of Bailey pairs where the exponent of q in αn is an indefinite quadratic form. As an application we obtain families of q-hypergeometric mock theta multisums.

On the rank of certain parametrized elliptic curves

In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.

Existence of an Algebra Norm on Certain Subalgebras of C(X)