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Author profile: Arias de Reyna Martínez, Juan
Institutional data
Name | Arias de Reyna Martínez, Juan |
Department | Análisis Matemático |
Knowledge area | Análisis Matemático |
Professional category | Investigador Honorario |
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Statistics
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No. publications
34
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No. visits
5982
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8397
Publications |
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Master's Final Project
Spaces of modular forms. Modular curves and dimensions
(2019)
The Modularity Theorem states that all rational elliptic curve arise from modular forms. In 1995, Andrew Wiles proved a ... |
Article
Tuples of polynomials over finite fields with pairwise coprimality conditions
(Elsevier, 2018)
Let q be a prime power. We estimate the number of tuples of degree bounded monic polynomials (Q1, . . . , Qv) ∈ (Fq[z])v ... |
Final Degree Project
Probabilidades y distribución de los números primos
(2017)
In this project, we will try to study the prime factors of a number taken at random. The main objective will be to introduce ... |
Article
On the distribution (mod 1) of the normalized zeros of the Riemann Zeta-function
(Elsevier, 2015)
We consider the problem whether the ordinates of the non-trivial zeros of ζ(s) are uniformly distributed modulo the Gram ... |
Article
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, ... |
Article
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 ... |
Article
Factor de impacto de largo alcance
(Real Sociedad Matemática Española, 2014)
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Chapter of Book
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 ... |
Article
Some bounds and limits in the theory of Riemann's zeta function
(Elsevier, 2012)
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, ... |
Article
A proof of a trigonometric inequality. A glimpse inside the mathematical kitchen
(2011)
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 ... |
Article
Asymptotics of Keiper-Li coefficients
(Adam Mickiewicz University, Faculty of Mathematics and Computer Science, 2011)
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, ... |
Article
Un primer encuentro con la Hipótesis de Riemann y su comprobación numérica
(Real Sociedad Matemática Española, 2010)
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Article
A test for the Riemann hypotesis
(Adam Mickiewicz University, 2008)
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 ... |
Article
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 ... |
Article
Dynamical zeta functions and Kummer congruences
(Seminarjum Matematyczne Uniwersytetu, 2005)
We establish a connection between the coefficients of Artin-Mazur zeta-functions and Kummer congruences. This allows to ... |
Article
Complejidad de los números naturales
(Real Sociedad Matemática Española, 2000)
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Article
Concentration of the distance in finite dimensional normed spaces
(University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics, 1998)
We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ∥x − y∥ is ... |
PhD Thesis
Propiedades de concentración en espacios de dimensión finita Inmersiones isométricas en espacios de funciones continuas
(1998)
Esta memoria está dedicada al estudio de dos problemas del Análisis Funcional: El estudio de propiedades de concentración ... |
PhD Thesis |
PhD Thesis
Rango y propiedades de medidas vectoriales. Conjuntos p-Sidon p.s.
(1991)
La presente memoria trata dos campos diferentes del Análisis Matemático. La primera parte se inscribe en el marco del ... |
PhD Thesis |
PhD Thesis
Espacios de sucesiones vectoriales
(1985)
Estudiamos en esta memoria dos problemas concretos sobre espacios de sucesiones vectoriales: Por un lado caracterizar las ... |
Article
I ∞ 0 (∑) no es totalmente tonelado
(Real Academia de Ciencias Exactas, Físicas y Naturales, 1985)
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. |
Article
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). |
Article
Non Baire measure spaces
(Institut de Matemàtica, Universitat de Barcelona, 1983)
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PhD Thesis
Teorema de Vitali-Hahn-Saks en álgebras de Boole
(1983)
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. |
Article
Definición y estudio de una función indefinidamente diferenciable de soporte compacto
(Real Academia de Ciencias Exactas, Físicas y Naturales, 1982)
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PhD Thesis |
PhD Thesis |
Article
Funciones derivables en cuaterniones
(Real Sociedad Matemática Española, 1975)
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Article
Álgebras de Abel cerradas
(Real Academia de Ciencias Exactas, Físicas y Naturales, 1975)
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Article
Integración en álgebras de Abel
(Real Academia de Ciencias Exactas, Físicas y Naturales, 1974)
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Article
Álgebras de Abel
(Real Academia de Ciencias Exactas, Físicas y Naturales, 1974)
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PhD Thesis |