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Rassias","submitted_at":"2017-05-28T09:40:13Z","abstract_excerpt":"A crucial role in the Nyman-Beurling-B\\'aez-Duarte approach to the Riemann Hypothesis is played by the distance \\[ d_N^2:=\\inf_{A_N}\\frac{1}{2\\pi}\\int_{-\\infty}^\\infty\\left|1-\\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 non-trivial zeros off the critical line. 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