Exceptional characters and prime numbers in short intervals

• John B. Friedlander ^[1] ; Henryk Iwaniec ^[2]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
  2. [2] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 10, Nº. 1, 2004, págs. 61-69
• Idioma: inglés
• DOI: 10.1007/s00029-004-0374-6
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Under the assumption of the Riemann hypothesis the asymptotic value y/log x is known to hold for the number of primes in the short interval [x - y, x] for y=xα for every fixed α<12 . We show under the assumption of the existence of exceptional Dirichlet characters the same asymptotic formula holds in the shorter intervals, for some α<12 \, in wide ranges of x depending on the characters.