Parametrizing elliptic curves by modular units

It is well-known that every elliptic curve over the rationals admits a parametrization by means of modular functions. In this short note, we show that only finitely many elliptic curves over $\mathbf{Q}$ can be parametrized by modular units. This answers a question raised by Zudilin in a recent work on Mahler measures. Further, we give the list of all elliptic curves $E$ of conductor up to $1000$ parametrized by modular units supported in the rational torsion subgroup of $E$. Finally, we raise several open questions.Comment: 7 pages, comments welcome

On the ramification of modular parametrizations at the cusps

We investigate the ramification of modular parametrizations of elliptic curves over Q at the cusps. We prove that if the modular form associated to the elliptic curve has minimal level among its twists by Dirichlet characters, then the modular parametrization is unramified at the cusps. The proof uses Bushnell's formula for the Godement-Jacquet local constant of a cuspidal automorphic representation of GL(2). We also report on numerical computations indicating that in general, the ramification index at a cusp seems to be a divisor of 24

Regulators of Siegel units and applications

We present a formula for the regulator of two arbitrary Siegel units in terms of L-values of pairwise products of Eisenstein series of weight one. We give applications to Boyd's conjectures and Zagier's conjectures for elliptic curves of conductor 14, 21, 35, 48 and 54.Comment: 19 page

Non-critical equivariant L-values of modular abelian varieties

We prove an equivariant version of Beilinson's conjecture on non-critical $L$-values of strongly modular abelian varieties over number fields. As an application, we prove a weak version of Zagier's conjecture on $L(E,2)$ and Deninger's conjecture on $L(E,3)$ for non-CM strongly modular $\mathbf{Q}$-curves.Comment: 18 page

Regulators for Rankin-Selberg products of modular forms

We prove a weak version of Beilinson's conjecture for non-critical values of $L$-functions for the Rankin-Selberg product of two modular forms.Comment: 16 pages, submitte

R\'egulateurs modulaires explicites via la m\'ethode de Rogers-Zudilin

We compute the regulator of Beilinson-Deninger-Scholl elements in terms of special values of L-functions of modular forms, using the Rogers-Zudilin method.Comment: 30 pages, in Frenc

Validation of the French Version of the Yale Food Addiction Scale: An Examination of Its Factor Structure, Reliability and Construct Validity in a Nonclinical Sample

International audienceObjective: Food addiction is a concept that has recently been proposed by applying the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision, criteria for substance dependence to eating behaviour. Food addiction has received increased attention given that it may play a role in binge eating, eating disorders, and the recent increase in obesity prevalence. Currently, there is no psychometrically sound tool for assessing food addiction in French. Our study aimed to test the psychometric properties of a French version of the Yale Food Addiction Scale (YFAS) by establishing its factor structure, internal consistency, and construct validity in a nonclinical population.Method: A total of 553 participants were assessed for food addiction (French version of the YFAS) and binge eating behaviour (Bulimic Investigatory Test, Edinburgh and Binge Eating Scale). We tested the scale’s factor structure (factor analysis for dichotomous data based on tetrachoric correlation coefficients), internal consistency, and construct validity with measures of binge eating.Results: Our results supported a 1-factor structure, which accounted for 54.1% of the variance. We demonstrated that this tool had adequate reliability and highly construct validity with measures of binge eating in this population, both in its diagnosis and symptom count version. A 2-factor structure explained an additional 9.1% of the variance, and could help to differentiate between patients with high, compared with low, levels of insight regarding addiction symptoms.Conclusions: In our study, we validated a psychometrically sound French version of the YFAS, both in its symptom count and diagnosis version. Future studies should validate this tool in clinical samples