On the arithmetic of a family of twisted constant elliptic curves

Let $\mathbb{F}_r$ be a finite field of characteristic $p>3$. For any power $q$ of $p$, consider the elliptic curve $E=E_{q,r}$ defined by $y^2=x^3 + t^q -t$ over $K=\mathbb{F}_r(t)$. We describe several arithmetic invariants of $E$ such as the rank of its Mordell--Weil group $E(K)$, the size of its N\'eron--Tate regulator $\text{Reg}(E)$, and the order of its Tate--Shafarevich group $III(E)$ (which we prove is finite). These invariants have radically different behaviors depending on the congruence class of $p$ modulo 6. For instance $III(E)$ either has trivial $p$-part or is a $p$-group. On the other hand, we show that the product $|III(E)|\text{Reg}(E)$ has size comparable to $r^{q/6}$ as $q\to\infty$, regardless of $p\pmod{6}$. Our approach relies on the BSD conjecture, an explicit expression for the $L$-function of $E$, and a geometric analysis of the N\'eron model of $E$.Comment: 38 pages. v2: minor changes following referee repor

Arithmetic and the standard electroweak theory

We propose the relations 1/e - e =3 and tan(2theta_W)=3/2, where e is the positron charge and theta_W is the weak angle. Present experimental data support these relations to a very high accuracy. We suggest that some duality relates the weak isospin and hypercharge gauge groups of the standard electroweak theory.Comment: Latex, 6 page

Search for the decay B+→K‾∗0K∗+B^+\rightarrow\overline{K}{}^{*0}K^{*+} at Belle

We report a search for the rare charmless decay $B^+\rightarrow\overline{K}{}^{*0}K^{*+}$ using a data sample of $772\times10^6$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. No statistically significant signal is found and a 90% confidence-level upper limit is set on the decay branching fraction as $\mathcal{B}(B^+\rightarrow\overline{K}{}^{*0}K^{*+}) <1.31\times 10^{-6}$.Comment: 8 pages, 3 figures, submitted to PRD(RC

Next-to-Leading-Order Corrections to the Production of Heavy-Flavour Jets in e+e- Collisions

In this paper we describe the calculation of the process e+e- -> Z/gamma -> QQbar + X, where Q is a heavy quark, at order alpha_s^2.Comment: 49 pages, Latex, epsfig, 6 figures. Tables 2 and 3 labels and captions have been fixe