Recent zbMATH articles in MSC 30H35https://www.zbmath.org/atom/cc/30H352022-05-16T20:40:13.078697ZWerkzeugRiesz projection and bounded mean oscillation for Dirichlet serieshttps://www.zbmath.org/1483.300092022-05-16T20:40:13.078697Z"Konyagin, Sergei"https://www.zbmath.org/authors/?q=ai:konyagin.sergey-v"Queffélec, Hervé"https://www.zbmath.org/authors/?q=ai:queffelec.herve"Saksman, Eero"https://www.zbmath.org/authors/?q=ai:saksman.eero"Seip, Kristian"https://www.zbmath.org/authors/?q=ai:seip.kristianSummary: We prove that the norm of the Riesz projection from \(L^\infty (\mathbb{T}^n)\) to \(L^p(\mathbb{T}^n)\) is \(1\) for all \(n\ge 1\) only if \(p\le 2\), thus solving a problem posed by \textit{J. Marzo} and the fourth author [Bull. Sci. Math. 135, No. 3, 324--331 (2011; Zbl 1221.42013)]. This shows that \(H^p(\mathbb{T}^{\infty})\) does not contain the dual space of \(H^1(\mathbb{T}^{\infty})\) for any \(p > 2\). We then note that the dual of \(H^1(\mathbb{T}^{\infty})\) contains, via the Bohr lift, the space of Dirichlet series in BMOA of the right half-plane. We give several conditions showing how this BMOA space relates to other spaces of Dirichlet series. Finally, relating the partial sum operator for Dirichlet series to Riesz projection on \(\mathbb{T}\), we compute its \(L^p\) norm when \(1 < p < \infty\), and we use this result to show that the \(L^\infty\) norm of the \(N\) th partial sum of a bounded Dirichlet series over \(d\)-smooth numbers is of order \(\log\log N\).On \(s\)-extremal Riemann surfaces of even genushttps://www.zbmath.org/1483.300792022-05-16T20:40:13.078697Z"Kozłowska-Walania, Ewa"https://www.zbmath.org/authors/?q=ai:kozlowska-walania.ewaSummary: We consider Riemann surfaces of even genus \(g\) with the action of the group \(\mathcal{D}_n\times \mathbb{Z}_2\), with \(n\) even. These surfaces have the maximal number of 4 non-conjugate symmetries and shall be called \textit{\(s\)-extremal}. We show various results for such surfaces, concerning the total number of ovals, topological types of symmetries, hyperellipticity degree and the minimal genus problem. If in addition an \(s\)-extremal Riemann surface has the maximal total number of ovals, then it shall simply be called \textit{extremal}. In the main result of the paper we find all the families of extremal Riemann surfaces of even genera, depending on if one of the symmetries is fixed-point free or not.