let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

Let $G$ be a group and $pi(G)$ be the set of primes $p$ such that $G$ contains an element of order $p$. Let $nse(G)$ be the set of the number of elements of the same order in $G$. In this paper, we prove that the simple group $L_2(p^2)$ is uniquely determined by $nse(L_2(p^2))$, where $pin{11,13}$‎.‎

We consider integrals of cuspforms f on reductive groups G defined over numberfields k against restrictions ι∗E of Eisenstein series E on “larger” reductive groups G̃ over k via imbeddings ι : G → G̃. We give hypotheses sufficient to assure that such global integrals have Euler products. At good primes, the local factors are shown to be rational functions in the corresponding parameters q−s from ...

Hepadnaviral reverse transcription occurs within cytoplasmic capsid particles and is catalyzed by a virally encoded reverse transcriptase, but the primary structure and multimeric state of the polymerase during reverse transcription are poorly understood. We measured these parameters for the duck hepatitis B virus polymerase employing active enzyme translated in vitro and derived from intracell...

Effects of morphologically related primes were examined in two masked prime experiments. Responses to both free root and derived suffixed word targets were facilitated when primes were derived suffixed words containing the target's root, and this facilitation effect showed a time course similar to that for the facilitation effect of repetition primes (though systematically smaller in magnitude)...

The transference principle of Green and Tao enabled various authors to transfer Szemer\'edi's theorem on long arithmetic progressions in dense sets sparse integers, mostly primes. In this paper, we provide a which applies general affine-linear configurations finite complexity. We illustrate the broad applicability our with case almost twin primes, by mean either Chen primes or "bounded gap prim...

To Paulo Ribenboim and his friends, the primes. 1. INTRODUCTION. It has long been known that there are infinitely many primes, and that there are infinitely many primes in any arithmetic progression a, a + d, a + 2d,. .. provided gcd(a, d) = 1 and d ≥ 1. If we ask slightly more involved questions, such as whether there exist infinitely many primes of the form n