In this paper, the zeros of linear combinations of the Riemann zeta function and its derivatives are studied. We establish an asymptotic formula for the number of zeros in a rectangle of height T. We also find a sharp asymptotic formula for the supremum of the real parts of zeros of such combinations in a certain family.
- Riemann zeta function
- linear combination of derivatives
- non-real zeros
ASJC Scopus subject areas
- Algebra and Number Theory