On Nyman, Beurling and Baez-Duarte’s Hilbert space reformulation of the Riemann hypothesis

On Beurling′s Real Variable Reformulatio

On Beurling′s Real Variable Reformulation of the Riemann Hypothesis

✍ L Baezduarte 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 623 KB

Let \(\rho(x)\) be the fractional part of \(x, B\) is the linear space of functions \(\sum_{1 \leqslant k \leqslant n} a_{k} \rho\left(\theta_{k} / x\right), \theta_{k} \in(0,1], \sum a_{k} \theta_{k}=0, n\) any positive integer. For \(p \in(1,2]\) Beurling proved that \(\zeta(s) \neq 0\) in \(\math