Asymptotic expansions, LL-values and a new Quantum Modular Form

In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function $F(q)$ of Kontsevich. Here we produce a new example of a quantum modular form by making use of some of Ramanujan's mock theta functions. Using these functions and their transformation behaviour, we also compute asymptotic expansions similar to expansions of $F(q)$.Comment: 7 page

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

On the arithmetic of a family of degree-two K3 surfaces

Let $\mathbb{P}$ denote the weighted projective space with weights $(1,1,1,3)$ over the rationals, with coordinates $x,y,z,$ and $w$; let $\mathcal{X}$ be the generic element of the family of surfaces in $\mathbb{P}$ given by \begin{equation*} X\colon w^2=x^6+y^6+z^6+tx^2y^2z^2. \end{equation*} The surface $\mathcal{X}$ is a K3 surface over the function field $\mathbb{Q}(t)$. In this paper, we explicitly compute the geometric Picard lattice of $\mathcal{X}$, together with its Galois module structure, as well as derive more results on the arithmetic of $\mathcal{X}$ and other elements of the family $X$.Comment: 20 pages; v2 with some all additions and clarifications suggested by the refere

DEA investment strategy in the Brazilian stock market

This paper presents a multi-period investment strategy using Data Envelopment Analysis (DEA) in the Brazilian stock market. Results show that the returns based on the DEA strategy were superior to the returns of a Brazilian stock index in most of the 22 quarters analyzed, presenting a significant Jensen's alpha.

The thickening of the thin disk in the third Galactic quadrant

In the third Galactic quadrant (180 < l < 270) of the Milky Way, the Galactic thin disk exhibits a significant warp ---shown both by gas and young stars--- bending down a few kpc below the formal Galactic plane (b=0). This warp shows its maximum at 240, in the direction of the Canis Major constellation. In a series of papers we have traced the detailed structure of this region using open star clusters, putting particular emphasis on the spiral structure of the outer disk. We noticed a conspicuous accumulation of young star clusters within 2-3 kpc from the Sun and close to b=0, that we interpreted as the continuation of the Local (Orion) arm towards the outer disk. While most clusters (and young stars in their background) follow closely the warp of the disk, our decade-old survey of the spiral structure of this region led us to identify three clusters, Haffner~18(1 and 2) and Haffner~19, which remain very close to b=0 and lie at distances (4.5, 8.0, and 6.4 kpc) where most of the material is already significantly warped. Here we report on a search for clusters that share the same properties as Haffner~18 and 19, and investigate the possible reasons for such an unexpected occurrence. We present UBVRI photometry of 5~young clusters, namely NGC~2345, NGC~2374, Trumpler~9, Haffner~20, and Haffner~21, which also lie close to the formal Galactic plane. With the exception of Haffner~20, in the background of these clusters we detected young stars that appear close to b=0, and are located at distances up to 8 kpc from the Sun, thus deviating significantly from the warp. These populations define a structure that distributes over almost the entire third Galactic quadrant. We discuss this structure in the context of a possible thin disk flaring, in full similarity with the Galactic thick disk.Comment: 53 pages, 12 eps figures, in press in the Astronomical Journa