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Artículo
Counting tuples restricted by pairwise coprimality conditions
(University of Waterloo, 2015)
Given a subset A of the set {1, . . . , v}2 we say that (a1, . . . , av) exhibits pairwise coprimality over A if gcd(ai, aj ) = 1 for all (i, j) ∈ A. For a given positive x and a given set A we give an asymptotic formula ...
Capítulo de Libro
On the sign of the real part of the Riemann zeta-function
(Springer, 2013)
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 ∈ [−T,+T] : |argζ(σ +it)| > π/2}|, and the closely related density d−(σ) = lim T→+∞ 1/2T |{t ∈ ...
Artículo
On the exact location of the non-trivial zeros of Riemann’s zeta function
(Polish Academy of Sciences, Institute of Mathematics, 2014)
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 − it) ζ 0( 1 2 + it) , (κ(0) = − 1 2 ). By studying the equation κ(t) = n ...
Artículo
On the distribution (mod 1) of the normalized zeros of the Riemann Zeta-function
(Elsevier, 2015-08)
We consider the problem whether the ordinates of the non-trivial zeros of ζ(s) are uniformly distributed modulo the Gram points, or equivalently, if the normalized zeros (xn) are uniformly distributed modulo 1. Odlyzko ...
Artículo
Funciones derivables en cuaterniones
(Real Sociedad Matemática Española, 1975)
Artículo
A test for the Riemann hypotesis
(Adam Mickiewicz University, 2008-09)
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 is some definite, computable real number (1.266 < J < 1.273). This provides us with a numerical test ...
Artículo
Non Baire measure spaces
(Institut de Matemàtica, Universitat de Barcelona, 1983)
Artículo
El problema onomástico para los ordinales numerables
(Real Academia de Ciencias Exactas, Físicas y Naturales, 1984)
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).
Artículo
Factor de impacto de largo alcance
(Real Sociedad Matemática Española, 2014)
Artículo
On some oscillating sums
(2008)
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 by a problem proposed by H. D. Ruderman [Problem 6105, Am. Math. Mon. 83, 573 (1977)] and solved ...