Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over Cp to subvarieties may be uniformly bounded. We prove this conjecture for torsion points on semi-abelian varieties over Qp using methods of algebraic model theory and a result of Sen on Galois representation of Hodge-Tate type. As a generalization of their theorem on linear forms in p-ad...

Abstract. We show that the fixed-point formula in an equivariant complex-oriented cohomology theory E, applied to the free loop space of a manifold X, defines a (renormalized) Riemann-Roch formula for the quotient of the group law of E by a free cyclic subgroup. If E is K-theory, this explains how the elliptic genus associated to the Tate elliptic curve emerges from Witten’s analysis of the fix...

Let E be an elliptic curve which is defined over Q and has stable reduction modulo a given prime p. Assuming that E is modular, one can associate to E a p-adic L-function Lp(E, s). (See [-Mz-SwD, A-V, Vi, Mz-T-T] for its construction in various cases.) This function is defined by a certain interpolation property and is analytic for seZp. In this paper, we will assume that E has split multiplica...

The Tate pairing has plenty of attractive applications, e.g., ID-based cryptosystems, short signatures, etc. Recently several fast implementations of the Tate pairing has been reported, which make it appear that the Tate pairing is capable to be used in practical applications. The computation time of the Tate pairing strongly depends on underlying elliptic curves and definition fields. However ...

Tate pairings has found several new applications in cryptography. However, how to compute Tate pairing is a research focus in all kinds of applications of pairing-based cryptosystems (PBC). In the paper, the structure of Miller’s algorithm is firstly analyzed, which is used to implement Tate pairing. Based on the characteristics that Miller’s algorithm will be improved tremendous if the order o...

One of the most valid and efficient models of long rod projectile penetration in homogeneous targets is Tate and Alekseevskii’s (A&t) model. Based on Tate’s model, the present research tries to calculate the optimum speeds to achieve the maximum penetration depth in the homogeneous targets. The proposed collision speed-penetration depth diagrams are developed using Tate’s model. In this way, va...