The Modularity Theorem states that all rational elliptic curve arise from modular forms. In 1995, Andrew Wiles proved a ...

Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v ...

In this project, we will try to study the prime factors of a number taken at random. The main objective will be to introduce ...

We consider the problem whether the ordinates of the non-trivial zeros of ζ(s) are uniformly distributed modulo the Gram ...

Given a subset A of the set {1, . . . , v}2 we say that (a1, . . . , av) exhibits pairwise coprimality over A if gcd(ai, ...

In this paper we introduce the real valued real analytic function κ(t) implicitly defined by e 2πiκ(t) = −e −2iϑ(t) ζ 0 ( 1 2 ...

We consider the distribution of argζ(σ +it) on fixed lines σ > 1/2, and in particular the density d(σ) = lim T→+∞ 1/2T |{t ...

For any real a > 0 we determine the supremum of the real σ such that ζ(σ+it) = a for some real t. For 0 < a < 1, a = 1, ...

We prove the inequality ∞ ∑ k=1(−1) k+1 rk cos kφ k+2 < ∞ ∑ k=1 (−1) k+1 rk k+2 for 0 < r 1 and 0 < φ < π . For the case ...

We show that the Riemann Hypothesis is equivalent to the assertion (ym)∈ℓ2 where ymym is defined by λm=1/2(logm+γ−log(2π)−1)+ym, ...

We prove that the Riemann Hypothesis holds if and only if I = Z +∞ 1 ˘ Π(x) − Li(x) ¯2 x −2 dx < +∞ with I = J, where J ...

This paper deals with the sums S α (n)=∑ j=1 n (-1) ⌊jα⌋ where α is any real number. The interest in these sums was initiated ...

We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to ...

We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ∥x − y∥ is ...

Esta memoria está dedicada al estudio de dos problemas del Análisis Funcional: El estudio de propiedades de concentración ...

La presente memoria trata dos campos diferentes del Análisis Matemático. La primera parte se inscribe en el marco del ...

Estudiamos en esta memoria dos problemas concretos sobre espacios de sucesiones vectoriales: Por un lado caracterizar las ...

Let ∑ be an infinite σ-field and denote by I ∞ 0 (∑) the space spanned by the characteristic functions of elements of ∑, endowed with the supremum norm. We prove that I ∞ 0 (∑) is not totally barrelled.

Assuming the existence of inaccesible cardinal numbers it is proved that there is not a notation, for each numerable ordinal number, satisfying the conditions imposed by N. Cuesta Dutari in his book La matemática del orden (1959).

El teorema de Vitali-Hahn-Saks sobre convergencia de medidas es probado para una nueva clase de álgebras de Boole definidas por una propiedad de separación de sus sucesiones disjuntas.