Extremal primes for elliptic curves without complex multiplication

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to the Hasse bound. Assuming that all the symmetric power L-functions associated to E are automorphic and satisfy the Generalized Riemann Hypothesis, we give the first non-trivial upper bounds for the number of such primes when E is a curve without complex multiplication. In order to obtain this bound, we use explicit equidistribution for the Sato-Tate measure as in the work of Rouse and Thorner (arXiv:1305.5283) and refine certain intermediate estimates taking advantage of the fact that extremal primes have a very small Sato-Tate measure

Joint Measurability and Temporal Steering

Quintino et. al. (Phys. Rev. Lett. 113, 160402 (2014)) and Uola et. al. (Phys. Rev. Lett. 113, 160403 (2014)) have recently established an intrinsic relation between non-joint measurability and Einstein-Podolsky- Rosen steering. They showed that a set of measurements is incompatible (i.e., not jointly measurable) if and only if it can be used for the demonstration of steering. In this paper, we prove the temporal analog of this result viz., a set of measurements are incompatible if and only if it exhibits temporal steering.Comment: 6 pages,no figures, typos corrected, improved presentation; To appear in JOSA B feature issue "80 years of Steering and the Einstein-Podolsky-Rosen Paradox

Writing a Life Between Gender Lines Conversations with A. Revathi about her autobiography The Truth About Me: A Hijra Life Story

A. Revathi was born physiologically male but felt and behaved like a girl - this is how she tells her story, as will be clear from the interview below. Nearly her whole childhood, spent in a village in Salem district of Tamil Nadu, was plagued by this deep and nagging unease of being trapped in the wrong body and by 'a growing sense of irrepressible femaleness'. But when she behaved like one of her girl-playmates, it only meant repeated humiliation and violence by her family and community. This affected her academic performance, and she had to drop out of school after failing the tenth grade. In a quest to be true to herself, Revathi, still in her teens, ran away from home and travelled to Delhi to join a house of hijras. Hijras are male-to-female transsexuals who undergo a surgical removal of the genitals (often performed surreptitiously and in unsanitary conditions) and comprise a distinct community across India with elaborate customs and regulations of their own. Hijras are given ritualistic importance by mainstream Indian society (for instance, their blessings are considered to bring good fortune) but at the same time they are easy targets for sexual crimes, discriminated against in public spaces, and have few options for livelihood apart from performing at social events, begging or prostitution. Revathi, now in her mid-forties, discusses all this with remarkable candour and courage in her autobiography The Truth About Me: A Hijra Life Story, translated into English from Tamil by V. Geetha and published by Penguin India Books in 2010. This autobiography is among the very first of its kind in India, uninhibited with regard to divisive gender lines, sexual hypocrisy of 'traditional' societies, and the dismal lack of public discourse on the rights of sexual minorities

Study on the Correlation Between Vitamin D and BMI in Type 2Diabetes Mellitus

Type 2 diabetes mellitus (DM) is associated with increased morbidity and mortality due to thedevelopment of complications, especially due to poor glycaemic control. Besides its role in calciumhomeostasis, Vitamin D has been involved in the pathophysiology as well as glycaemic control oftype 2 DM. 100 patients diagnosed with type 2 DM were included. Vitamin D levels along with BMIwere measured in all the individuals. In our study, we had the youngest patient with 18years andthe oldest patient with 78years. In the present study, we had maximum patients in the age groupbetween 41 to 50 years similar to various other studies. In our study male was 68% with femaleswere 38%. In the present study, we estimated vitamin D levels in all subjects and categorizationwas done as <20 and more than 20 ng/dl.48% of patients had vitamin D levels below 20ng/dl. Inthe present study, we compared the values of BMI with vitamin D levels where we did not noticemuch difference with the mean of individual category. In conclusion, we have identified a correlationconcerning vitamin D levels when compared with BMI statistically. Since the physiological role ofVitamin D in pancreatic beta-cell function and insulin sensitivity is well appreciated, and consideringthat almost 50% of the diabetes patients in the present study are Vitamin D deficient, it issuggested that Vitamin D levels improve the BMI in type 2 diabetes mellitus patient

Collective multipole-like signatures of entanglement in symmetric N-qubit systems

A cogent theory of collective multipole-like quantum correlations in symmetric multiqubit states is presented by employing SO(3) irreducible spherical tensor representation. An arbitrary bipartite division of this system leads to a family of inequalities to detect entanglement involving averages of these tensors expressed in terms of the total system angular momentum operator. Implications of this theory to the quantum nature of multipole-like correlations of all orders in the Dicke states are deduced. A selected set of examples illustrate these collective tests. Such tests detect entanglement in macroscopic atomic ensembles, where individual atoms are not accessible.Comment: REVTEX, 4 pages with 1 figure; To appear in Phys. Rev.

Local Invariants and Pairwise Entanglement in Symmetric Multi-qubit System

Pairwise entanglement properties of a symmetric multi-qubit system are analyzed through a complete set of two-qubit local invariants. Collective features of entanglement, such as spin squeezing, are expressed in terms of invariants and a classifcation scheme for pairwise entanglement is proposed. The invariant criteria given here are shown to be related to the recently proposed (Phys. Rev. Lett. 95, 120502 (2005)) generalized spin squeezing inequalities for pairwise entanglement in symmetric multi-qubit states.Comment: 9 pages, 2 figures, REVTEX, Replaced with a published versio

Equidistribution of p alpha p theta with a Chebotarev condition and applications to

We establish a joint distribution result concerning the fractional part of $\alpha p^\theta$ for $\theta \in (0,1), \ \alpha>0$, where $p$ is a prime satisfying a Chebotarev condition in a fixed finite Galois extension over $\mathbb{Q}$. As an application, for a fixed non-CM elliptic curve $E/\mathbb{Q}$, an asymptotic formula is given for the number of primes at the extremes of the Sato-Tate measure modulo a large prime $\ell$. These are precisely the primes $p$ for which the Frobenius trace $a_p(E)$ satisfies the congruence $a_p(E)\equiv [2\sqrt{p}] \bmod \ell$. We assume a zero-free region hypothesis for Dedekind zeta functions of number fields