2011/08/08 by J. S. Dowker, Dowker, J. S. · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Nonlinear Waves and Solitons #Polynomial and algebraic computation #hep-th #math-ph #math.MP #math.NT
paper · pdf · doi:10.48550/arxiv.1108.1760
24 pages
arxiv created 2011/08/08 · arxiv updated 2011/08/09
I show for the specific case of the scalar field spectrum on regular tessellations of the sphere that the first two terms of the heat--kernel expansion are related to the first two terms of the Ehrhart (quasi)polynomial. In trying to make this relation precise, I consider degeneracies as partition denumerants and show the connection of the group theory expressions with Popoviciu's theorem and with the notion of Sylvester waves. General denumerants are considered and the first wave, i.e. the polynomial part, is written using the A-genus multiplicative sequence. It is pointed out that Sylvester in effect did the same thing and that he had also obtained Ehrhart reciprocity. I derive an algebraically neat form for the second wave which involves the combination of two multiplicative sequences.