Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
Self-reciprocal polynomials over finite fields.
Sequences of reducible -polynomials modulo a prime.
Shtukas and Jacobi sums.
Sidon basis in polynomial rings over finite fields
Let denote the polynomial ring over , the finite field of elements. Suppose the characteristic of is not or . We prove that there exist infinitely many such that the set contains a Sidon set which is an additive basis of order .
Singular moduli and supersingular moduli of Drinfeld modules.
Solving quadratic equations over polynomial rings of characteristic two.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1,...
Some Algebraic Properties of Polynomial Rings
In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
Some congruences for binomial coefficients
Some doubly exponential sums over ℤₘ
Some generalisations of Chebyshev polynomials and their induced group structure over a finite field
Some inequalities in functional analysis, combinatorics, and probability theory.
Some new Results for Additive Self-Dual Codes over GF(4)
* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.Additive code C over GF(4) of length n is an additive subgroup of GF(4)n. It is well known [4] that the problem of finding stabilizer quantum error-correcting codes is transformed into problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to construct good additive self-dual codes of length 13...
Some problems in multidimensional analytic number theory
Somme des chiffres et transcendance
Sommes de carrés dans [Book]
Sommes de carrés de polynômes irréductibles dans
Sommes de carrés et d’irréductibles dans
Sommes de cubes dans l’anneau
Sommes de deux carrés dans et problèmes de diviseurs