Explicit formula for coefficients of Todd series of lattice cones

Hi-joon Chae; Byungheup Jun; Jungyun Lee

doi:10.4134/CKMS.2015.30.2.73

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2015; 30(2): 73-79

Printed April 30, 2015

https://doi.org/10.4134/CKMS.2015.30.2.73

Explicit formula for coefficients of Todd series of lattice cones

Hi-joon Chae, Byungheup Jun, and Jungyun Lee

Hongik University, UNIST, Ewha Womans University

Abstract

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Abstract

Todd series are associated to maximal non-degenerate lattice cones. The coefficients of Todd series of a particular class of lattice cones are closely related to generalized Dedekind sums of higher dimension. We generalize this construction and obtain an explicit formula for coefficients of the Todd series. It turns out that every maximal non-degenerate lattice cone, hence the associated Todd series can be obtained in this way.

Keywords: Dedekind sum, lattice cone, Todd series

MSC numbers: 11F20, 11H06, 11P21