• Artin’s Conjecture on primes with prescribed primitive roots 

      López-Contreras González, Javier (Universitat Politècnica de Catalunya, 2023-05-30)
      Treball Final de Grau
      Accés obert
      Realitzat a/amb:   University of California, Berkeley
      La Conjectura d’Artin sobre la densitat del conjunt de nombres primers amb una arrel primitiva prescrita és un dels problemes matemàtics oberts més fàcils d’enunciar. En la seva versió més clàssica, es planteja la següent ...
    • Every integer can be written as a square plus a squarefree 

      Jiménez Urroz, Jorge (2022-09)
      Article
      Accés restringit per política de l'editorial
      In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in ...
    • Primes represented by quadratic polynomials via exceptional characters 

      Chamizo Lorente, Fernando; Jiménez Urroz, Jorge (Springer Nature, 2021-08-01)
      Article
      Accés obert
      We estimate the number of primes represented by a general quadratic polynomial with discriminant ¿, assuming that the corresponding real character is exceptional.
    • Product of primes in arithmetic progressions 

      Ramaré, Olivier; Srivastav, Priyamvad; Serra Albó, Oriol (2020-05-01)
      Article
      Accés obert
      We prove that, for all q=2 and for all invertible residue classes a modulo q, there exists a natural number n=(650q)9 that is congruent to a modulo q and that is the product of exactly three primes, all of which are below ...
    • The Prime number theorem for L-functions of elliptic curves with CM 

      Grados Fukuda, Miguel Daygoro (Universitat Politècnica de Catalunya, 2012-07)
      Projecte Final de Màster Oficial
      Accés obert
      A través de un ejemplo de curva elíptica con CM, definimos L(E,s), su función L asociada. Luego, veremos cómo esta función proviene de un caracter de Hecke, y tras un breve estudio de las funciones L en un contexto general, ...
    • The Riemann zeta function and its applications 

      Hernández Barrios, Víctor (Universitat Politècnica de Catalunya, 2017-07)
      Treball Final de Grau
      Accés obert
      The aim of this thesis is to expose the basic theory of the Riemann zeta function and some of its classical applications in multiplicative number theory, like the prime number theorem and Dirichlet's theorem on arithmetic ...