On certain plane curves with many integral points.
Convergence acceleration of alternating series.
On the square root of special values of certain L-series.
Counting colorings on varieties.
We present a combinatorial mechanism for counting certain objects associated to a variety over a finite field. The basic example is that of counting conjugacy classes of the general linear group. We discuss how the method applies to counting these and also to counting unipotent matrices and pairs of commuting matrices.
[Proceedings of the
Concordant sequences and integral-valued entire functions
A classic theorem of Pólya shows that the function is the “smallest” integral-valued entire transcendental function. A variant due to Gel’fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin’s result together with a further generalization.
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