On the zeros of linear combinations of derivatives of the Riemann zeta function, II

被引：0

作者：

Koutsaki, K. Paolina ^{[1
]}

Tamazyan, Albert ^{[1
]}

Zaharescu, Alexandru ^{[1
,2
]}

机构：

[1] Univ Illinois, Dept Math, 1409 West Green St, Urbana, IL 61801 USA

[2] Romanian Acad, Simion Stoilow Inst Math, POB 1-764, RO-014700 Bucharest, Romania

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2018年 / 14卷 / 02期

关键词：

Riemann zeta function; relevant numbers; linear combination of derivatives;

D O I：

10.1142/S1793042118500252

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The relevant number to the Dirichlet series G(s) = Sigma(infinity)(n=1) a(n) n(-s) , is defined to be the lo log n unique integer a with a(n) not equal 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.

引用

页码：371 / 382

页数：12