La Cyclotomie Jadis Et Naguère (cyclotomy past and Present?) by Andrè Weil

Using of Generalized Cyclotomy for Sequence Design over the Finite Field of Order Four with High Linear Complexity

We consider the use of generalized Ding-Helleseth cyclotomy to design sequences over the finite field of order four. Using generalized cyclotomic classes of order four we obtain the family of balanced sequences of odd period with high linear complexity. Also we present a method of constructing sequences with high linear complexity and arbitrary even period over the finite field of order four. T...

Cyclotomy of Weil Sums of Binomials

The Weil sum WK,d(a) = ∑ x∈K ψ(x d + ax) where K is a finite field, ψ is an additive character of K, d is coprime to |K|, and a ∈ K arises often in number-theoretic calculations, and in applications to finite geometry, cryptography, digital sequence design, and coding theory. Researchers are especially interested in the case where WK,d(a) assumes three distinct values as a runs through K. A Gal...

First steps towards p-adic Langlands functoriality

— By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modification of the classical local Langlands correspondence, we associate with any pair consisting of a Weil-Deligne group representation and a type ...

SMALLPOX AND MEASLES AS DESCRIBED BY RAZI (LE LIVER SUR LA V ARIOLE ET LA ROUGEOLE)

ON CURVES OVER FINITE FIELDS by

— In these notes we present some basic results of the Theory of Curves over Finite Fields. Assuming a famous theorem of A. Weil, which bounds the number of solutions in a finite field (i.e., number of rational points) in terms of the genus and the cardinality of the finite field, we then prove several other related bounds (bounds of Serre, Ihara, Stohr-Voloch, etc.). We then treat Maximal Curve...