arXiv subjects

Alexander Molnar

Publications and source records attributed to Alexander Molnar.

2 recordsLinked to original sources

arXiv2015

Arithmetic and intermediate Jacobians of some rigid Calabi-Yau threefolds

We construct Calabi-Yau threefolds defined over $\mathbb{Q}$ via quotients of abelian threefolds, and re-verify the rigid Calabi-Yau threefolds in this construction are modular by computing their L-series, without \cite{Dieulefait} or \cite{GouveaYui}. We compute the intermediate Jacobians of the rigid Calabi-Yau threefolds as complex tori, then compute a $\mathbb{Q}$-model for the 1-torus given a $\mathbb{Q}$-structure on the rigid Calabi-Yau threefolds, and find infinitely many examples and counterexamples for a conjecture of Yui about the relation between the $L$-series of the rigid Calabi-Yau threefolds and the $L$-series of their intermediate Jacobians.

math.NT↗

arXiv2012

Minimal models for rational functions in a dynamical setting

We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational coefficients that have many integers in a single orbit. We find several minimal quadratic rational functions with 8 integers in an orbit and several minimal cubic rational functions with 10 integers in an orbit. We also make some elementary observations on possibilities of an analogue of Szpiro's conjecture in a dynamical setting and on the structure of the set of minimal models for a given rational function.

math.NT↗