On the zeros of linear combinations of derivatives of the Riemann zeta function, II
2018 ◽
Vol 14
(02)
◽
pp. 371-382
Keyword(s):
The Real
◽
The relevant number to the Dirichlet series [Formula: see text], is defined to be the unique integer [Formula: see text] with [Formula: see text], which maximizes the quantity [Formula: see text]. In this paper, we classify the set of all relevant numbers to the Dirichlet [Formula: see text]-functions. The zeros of linear combinations of [Formula: see text] 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.
2016 ◽
Vol 12
(06)
◽
pp. 1703-1723
◽
Keyword(s):
Keyword(s):
Keyword(s):
2013 ◽
Vol 25
(2)
◽
pp. 285-305
◽
Keyword(s):
1988 ◽
Vol 28
(4)
◽
pp. 115-124
Keyword(s):
1984 ◽
Vol 19
(1)
◽
pp. 85-102
◽
Keyword(s):
2011 ◽
Vol 131
(10)
◽
pp. 1939-1961
◽
Keyword(s):