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Rational isogenies of prime degree
In this table, g is the genus of Xo(N), and v the number of noncuspidal rational points of Xo(N) (which is, in effect, the number of rational N-isogenies classified up to "twist"). For an excellent
An algebraic method for public-key cryptography
Algebraic key establishment protocols based on the difficulty of solving equations over algebraic structures are described as a theoretical basis for constructing public–key cryptosystems.
Automorphic Forms and L-Functions for the Group Gl(n, R)
Introduction 1. Discrete group actions 2. Invariant differential operators 3. Automorphic forms and L-functions for SL(2,Z) 4. Existence of Maass forms 5. Maass forms and Whittaker functions for
New Key Agreement Protocols in Braid Group Cryptography
Key agreement protocols are presented whose security is based on the difficulty of inverting one-way functions derived from hard problems for braid groups. Efficient/low cost algorithms for key
The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer
L’accès aux archives de la revue « Annali della Scuola Normale Superiore di Pisa, Classe di Scienze » (http://www.sns.it/it/edizioni/riviste/annaliscienze/) implique l’accord avec les conditions
Voronoi formulas on GL(n)
In this paper, we give a new, simple, purely analytic proof of the Voronoi formula for Maass forms on GL(3) first derived by Miller and Schmid. Our method is based on two lemmas of the first author
Multiple Dirichlet Series and Moments of Zeta and L-Functions
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward