Non-vanishing of LL-functions associated to cusp forms of half-integral weight

In this article, we prove non-vanishing results for $L$-functions associated to holomorphic cusp forms of half-integral weight on average (over an orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings (Springer

On certain finiteness questions in the arithmetic of modular forms

We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N, m, and prime p with p not dividing N, there is only a finite number of reductions modulo p^m of normalized eigenforms on \Gamma_1(N). We consider various variants of our basic finiteness conjecture, prove a weak version of it, and give some numerical evidence.Comment: 25 pages; v2: one of the conjectures from v1 now proved; v3: restructered parts of the article; v4: minor corrections and change

Singular values of some modular functions

We study the properties of special values of the modular functions obtained from Weierstrass P-function at imaginary quadratic points.Comment: 19 pages,corrected typo

Drosophila Parkin requires PINK1 for mitochondrial translocation and ubiquitinates Mitofusin

Loss of the E3 ubiquitin ligase Parkin causes early onset Parkinson's disease, a neurodegenerative disorder of unknown etiology. Parkin has been linked to multiple cellular processes including protein degradation, mitochondrial homeostasis, and autophagy; however, its precise role in pathogenesis is unclear. Recent evidence suggests that Parkin is recruited to damaged mitochondria, possibly affecting mitochondrial fission and/or fusion, to mediate their autophagic turnover. The precise mechanism of recruitment and the ubiquitination target are unclear. Here we show in Drosophila cells that PINK1 is required to recruit Parkin to dysfunctional mitochondria and promote their degradation. Furthermore, PINK1 and Parkin mediate the ubiquitination of the profusion factor Mfn on the outer surface of mitochondria. Loss of Drosophila PINK1 or parkin causes an increase in Mfn abundance in vivo and concomitant elongation of mitochondria. These findings provide a molecular mechanism by which the PINK1/Parkin pathway affects mitochondrial fission/fusion as suggested by previous genetic interaction studies. We hypothesize that Mfn ubiquitination may provide a mechanism by which terminally damaged mitochondria are labeled and sequestered for degradation by autophagy

Barcoding life to conserve biological diversity: Beyond the taxonomic imperative

Barcoding scientists aspire to adhere to the objectives of the Convention on Biological Diversity by promoting conservation, sustainability, and the equitable sharing of benefits arising from use of genetic resources. (Image: Juan Manuel Escalante, wwww.realitat.com

A look with BeppoSAX at the low-luminosity Galactic X-ray source 4U 2206+54

A pointed observation of the low-luminosity galactic source 4U 2206+54 was carried out in November 1998 with BeppoSAX. The light curve of 4U 2206+54 shows erratic variability on a timescale of about 1 hour; neither hardness variations nor time periodicities are detected throughout this 67 ks long observation. Thanks to the wide spectral coverage capabilities of BeppoSAX we could observe the source X-ray continuum over three energy decades, from 0.6 to 60 keV. The spectrum could be equally well fitted either with a blackbody plus Comptonization or with a high energy cutoff power law. No iron emission around 6.5 keV was detected, while a tentative detection of a cyclotron resonant feature in absorption is presented. Comparison of the present BeppoSAX data with the information available in the literature for this source suggests that 4U 2206+54 is a close binary system in which a (possibly magnetized) NS is accreting from the companion star wind.Comment: 9 pages, 5 figures, 2 tables; accepted for publication on Astronomy & Astrophysics, main journal. Final version of the paper including the A&A Language Editor's comment

Functional central limit theorems for vicious walkers

We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval $(0,T]$ for the first type and in an infinite time interval $(0,\infty)$ for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publicatio

Amicable pairs and aliquot cycles for elliptic curves

An amicable pair for an elliptic curve E/Q is a pair of primes (p,q) of good reduction for E satisfying #E(F_p) = q and #E(F_q) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j not 0) have no aliqout cycles of length greater than two. We give conjectural formulas for the frequency of amicable pairs. For CM curves, the derivation of precise conjectural formulas involves a detailed analysis of the values of the Grossencharacter evaluated at a prime ideal P in End(E) having the property that #E(F_P) is prime. This is especially intricate for the family of curves with j = 0.Comment: 53 page

The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change