Resumen de Exceptional characters and prime numbers in short intervals

John B. Friedlander, Henryk Iwaniec

• 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.