The relevant number to the Dirichlet series G(s) = Σn=1∞ ann-s, is defined to be the unique integer n with an ≠ 0, which maximizes the quantity log log n log n. In this paper, we classify the set of all relevant numbers to the Dirichlet L-functions. The zeros of linear combinations of G and its derivatives are also studied. We give an asymptotic formula for the supremum of the real parts of zeros of such combinations. We also compute the degree of the largest derivative needed for such a combination to vanish at a certain point.
- Riemann zeta function
- linear combination of derivatives
- relevant numbers
ASJC Scopus subject areas
- Algebra and Number Theory