Construction of elliptic $\mathfrak{p}$-units

Elliptic units for real quadratic fields

1. A review of the classical setting 2. Elliptic units for real quadratic fields 2.1. p-adic measures 2.2. Double integrals 2.3. Splitting a two-cocycle 2.4. The main conjecture 2.5. Modular symbols and Dedekind sums 2.6. Measures and the Bruhat-Tits tree 2.7. Indefinite integrals 2.8. The action of complex conjugation and of Up 3. Special values of zeta functions 3.1. The zeta function 3.2. Va...

Pseudo-elliptic Integrals, Units, and Torsion

We remark on pseudo-elliptic integrals and on exceptional function fields, namely function fields defined over an infinite base field but nonetheless containing non-trivial units. Our emphasis is on some elementary criteria that must be satisfied by a squarefree polynomial D.x/ whose square root generates a quadratic function field with non-trivial unit. We detail the genus 1 case. 2000 Mathema...

Construction of Pairing-Friendly Elliptic Curves

The aim of this paper is to construct pairing friendly elliptic curves. In this paper, we explain a method of finding the polynomials representing √−D and ζk over the field containing √−D and ζk and how to construct a pairing friendly elliptic curves over the cyclotomic fields containing Q(ζk, √−D) for arbitrary k and D by CP method. By using the factorization of the cyclotomic polynomial combi...

Efficient Construction of Cryptographically Strong Elliptic Curves

Simple Construction of Elliptic Boundary K - matrix ¶

We give the infinite-dimensional representation for the ellipticK-operator satisfying the boundary Yang-Baxter equation. By restricting the functional space to finite-dimensional space, we construct the elliptic K-matrix associated to Belavin’s completely Z-symmetric R-matrix. PACS: ¶ arch-ive/9507123 † [email protected] 1 The quantum R-matrix as solutions of the Yang-Baxter equ...