Hypergeometric L-functions in average polynomial time

We describe an algorithm for computing, for all primes $p \leq X$, the mod-$p$ reduction of the trace of Frobenius at $p$ of a fixed hypergeometric motive in time quasilinear in $X$. This combines the Beukers--Cohen--Mellit trace formula with average polynomial time techniques of Harvey et al.Comment: 15 pages, 1 figure; v4 several exposition improvements as suggested the referee

Solvent effects on the properties of hyperbranched polythiophenes

The structural and electronic properties of all-thiophene dendrimers and dendrons in solution have been evaluated using very different theoretical approaches based on quantum mechanical (QM) and hybrid QM/molecular mechanics (MM) methodologies: (i) calculations on minimum energy conformations using an implicit solvation model in combination with density functional theory (DFT) or time-dependent DFT (TD-DFT) methods; (ii) hybrid QM/MM calculations, in which the solute and solvent molecules are represented at the DFT level as point charges, respectively, on snapshots extracted from classical molecular dynamics (MD) simulations using explicit solvent molecules, and (iii) QM/MM-MD trajectories in which the solute is described at the DFT or TD-DFT level and the explicit solvent molecules are represented using classical force-fields. Calculations have been performed in dichloromethane, tetrahydrofuran and dimethylformamide. A comparison of the results obtained using the different approaches with the available experimental data indicates that the incorporation of effects associated with both the conformational dynamics of the dendrimer and the explicit solvent molecules is strictly necessary to satisfactorily reproduce the properties of the investigated systems. Accordingly, QM/MM-MD simulations are able to capture such effects providing a reliable description of electronic properties–conformational flexibility relationships in all-Th dendrimers.Peer ReviewedPostprint (author's final draft

Aircraft clouds: from chemtrail pseudoscience to the science of contrails

The most frequent statements and arguments found in pseudoscience websites and forums supporting the existence of so-called aircraft chemtrails can be refuted with a scientific explanation of the processes resulting in the formation of condensation or deposition trails, known as contrails. Thus, the hypothesis that chemtrails exist is disproven by the scientific literature that shows that they are the exact same entity as contrails: They are hydrological phenomena which result from a physical process referenced in the many studies carried out since the beginning of the age of aviation, in the early twentieth century. Hence, in this paper we conclude that pseudoscience’s chemtrails are nothing more than the contrails described by science.Peer ReviewedVersió final publicad