Small gaps in coefficients of -functions and -free numbers in short intervals.
This paper studies integer solutions to the equation in which none of have a large prime factor. We set , and consider primitive solutions () having no prime factor larger than , for a given finite . We show that the Conjecture implies that for any fixed the equation has only finitely many primitive solutions. We also discuss a conditional result, showing that the Generalized Riemann hypothesis (GRH) implies that for any fixed the equation has infinitely many primitive solutions....
We solve a problem of Bombieri, stated in connection with the «prime number theorem» for function fields.