LECTURE 1 RESIDUE FORMULAE FOR BERNOULLI POLYNOMIALS AND VERLINDE SUMS

Michèle Vergne
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Michèle Vergne: Centre de Mathematiques, Ecole Polytechnique, F-91128 Palaiseau Cedex, France

Chapter 13 in European Women in Mathematics, 2003, pp 227-244 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe discuss some of the properties of the Bernoulli series\[{{B(p,t)}\over{p!}} = - \sum\limits_{n \ne 0}{{{e^{2i\pi nt}}\over{(2i\pi n)^p}}}\] and higher dimensional analogues, the Witten series. Similarly, we discuss trigonometric series\[V(q,k) = \sum\limits_{n = 1}^{k - 1} {{1\over{4^q (\sin (\pi n/k))^{2q}}}\]and higher dimensional analogues, the Verlinde sums. We deduce the polynomial feature of these expressions, from multidimensional residues expressions due to A. Szenes.

Keywords: Mathematical Finance; Geometry; Cohomology (search for similar items in EconPapers)
Date: 2003
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