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Author's Draft
On the size of an expression in the NymanBeurlingBáezDuarte criterion for the Riemann Hypothesis


Helmut Maier,
Department of Mathematics, University of Ulm, Helmholtzstrasse 18, 89081 Ulm, Germany
Michael Th. Rassias,
Institute of Mathematics, University of Zurich, CH8057, Zurich, Switzerland
Abstract
A crucial role in the NymanBeurlingBáezDuarte approach to
the Riemann Hypothesis is played by the distance
\[
d_N^2:=\inf_{A_N}\frac{1}{2\pi}\int_{\infty}^\infty
\left1\zeta A_N
\left(\frac{1}{2}+it
\right)
\right^2\frac{dt}{\frac{1}{4}+t^2}\:,
\]
where the infimum is over all Dirichlet polynomials
$$A_N(s)=\sum_{n=1}^{N}\frac{a_n}{n^s}$$
of length $N$.
In this paper we investigate $d_N^2$ under the assumption that
the Riemann zeta function has four nontrivial zeros off the
critical line.
MSC Classifications: 
30C15, 11M26 show english descriptions
Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
30C15  Zeros of polynomials, rational functions, and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) {For algebraic theory, see 12D10; for real methods, see 26C10} 11M26  Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
