 CARMA ANALYSIS AND NUMBER THEORY SEMINAR
 Speaker: Dr James Wan, Singapore University of Technology and Design
 Title: Sums of Double Zeta Values
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 1:00 pm, Tue, 12^{th} Jun 2012
 Abstract:
The double zeta values are one natural way to generalise the Riemann zeta function at the positive integers; they are defined by $\zeta(a,b) = \sum_{n=1}^\infty \sum_{m=1}^{n1} 1/n^a/m^b$. We give a unified and completely elementary method to prove several sum formulae for the double zeta values. We also discuss an experimental method for discovering such formulae.
Moreover, we use a reflection formula and recursions involving the Riemann zeta function to obtain new relations of closely related functions, such as the Witten zeta function, alternating double zeta values, and more generally, character sums.
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 CARMA ANALYSIS AND NUMBER THEORY SEMINAR
 Speaker: Dr James Wan, Singapore University of Technology and Design
 Title: Legendre polynomials and Ramanujantype series for $1/\pi$
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:30 pm, Tue, 10^{th} May 2011
 Abstract:
We resolve some recent and fascinating conjectural formulae for $1/\pi$ involving the Legendre polynomials. Our mains tools are hypergeometric series and modular forms, though no prior knowledge of modular forms is required for this talk. Using these we are able to prove some general results regarding generating functions of Legendre polynomials and draw some unexpected number theoretic connections.
This is joint work with Heng Huat Chan and Wadim Zudilin. The authors dedicate this paper to Jon Borwein's 60th birthday.
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 CARMA ANALYSIS AND NUMBER THEORY SEMINAR
 Speaker: Dr James Wan, Singapore University of Technology and Design
 Title: Moments of elliptic integrals
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Time and Date: 3:30 pm, Wed, 24^{th} Nov 2010
 Abstract:
The complete elliptic integrals of the first and second kinds (K(x) and E(x)) will be introduced and their key properties revised. Then, new and perhaps interesting results concerning moments and other integrals of K(x) and E(x) will be derived using elementary means. Diverse connections will be made, for instance with random walks and some experimental number theory.
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