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- Title
On the zeros of linear combinations of derivatives of the Riemann zeta function, II.
- Authors
Koutsaki, K. Paolina; Tamazyan, Albert; Zaharescu, Alexandru
- Abstract
The relevant number to the Dirichlet series , is defined to be the unique integer with , which maximizes the quantity . In this paper, we classify the set of all relevant numbers to the Dirichlet -functions. The zeros of linear combinations of 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.
- Subjects
LINEAR complexes; LINEAR systems; MATHEMATICAL combinations; DERIVATIVES (Mathematics); RIEMANNIAN geometry; ZETA functions
- Publication
International Journal of Number Theory, 2018, Vol 14, Issue 2, p371
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042118500252