Type: Article

Some remarks on the Riemann zeta function and prime factors of numerators of Bernoulli numbers

Luca, Florian; Pizarro-Madariaga, Amalia;

Abstract:

We prove that the sequence {log zeta(n)}(n >= 2) is not holonomic, that is, does not satisfy a finite recurrence relation with polynomial coefficients. A similar result holds for L-functions. We then prove a result concerning the number of distinct prime factors of the sequence of numerators of even indexed Bernoulli numbers.