arXiv subjects

Fernando Rodriguez Villegas

Publications and source records attributed to Fernando Rodriguez Villegas.

24 records · Page 2Linked to original sources

arXiv2007

Integral ratios of factorials and algebraic hypergeometric functions

Sketch of proof of a theorem relating the two subjects of the title. It can be thought as an extension of results of Landau for the classical hypergeometric function. It relies on the characterization of algebraic hypergeometric functions of Beukers and Heckman. In the process we also show that a variant of a classical construction of Bezout (producing a quadratic form, the Bezoutian, out of two polynomials in one variable) gives the Hermitian form fixed by the monodromy group, up to scaling.

math.NT↗

arXiv2006

Counting colorings on varieties

The goal of this note is to present a combinatorial mechanism for counting certain objects associated to a variety X defined over a finite field. The basic example is that of counting conjugacy classes in GL_n(F_q), where X is the multiplicative group.

math.NT↗

arXiv2006

Explicit models of genus 2 curves with split CM

We outline a general algorithm for computing an explicit model over a number field of any curve of genus 2 whose (unpolarized) Jacobian is isomorphic to the product of two elliptic curves with CM by the same order in an imaginary quadratic field. We give the details and some examples for the case where the order has prime discriminant and class number one

math.NT↗

arXiv2006

Computing central values of $L$-functions

This is a mostly expository note concerning the following question: How fast can we compute the value of an L-function at the center of the critical strip? It is the writeup of my talk at the Matrix Ensembles and L-Functions workshop at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK on July 2005.

math.NT↗

arXiv2006

Identities between Mahler measures

The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures m(y^2+2xy+y-x^3-2x^2-x)=5/7*m(y^2+4xy+y-x^3+x^2) which is one of many examples that arise from the comparison of Mahler measures and special values of L-functions.

math.NT↗

arXiv2004

Lattice polytopes, Hecke operators, and the Ehrhart polynomial

Let P be a simple lattice polytope. We define an action of the Hecke operators on E (P), the Ehrhart polynomial of P, and describe their effect on the coefficients of E (P). We also describe how the Brion-Vergne formula transforms under the Hecke operators for nonsingular lattice polytopes P.

math.CO↗