In this paper, we propose a new representation of numeric functions using a piecewise arithmetic expression. To represent a numeric function compactly, we partition the domain of the function into uniform segments, and transform the sub-function in each segment into an arithmetic spectrum. From this arithmetic spectrum, we derive an arithmetic expression, and obtain a piecewise arithmetic expre...

Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the...

This is a brief report on recent work of the author (some joint with Greg Anderson) and his student on multizeta values for function fields. This includes definitions, proofs and conjectures on the relations, period interpretation in terms of mixed CarlitzTate t-motives and related motivic aspects. We also verify Taelman’s recent conjectures in special cases. 2010 Mathematics Subject Classifica...