Recent zbMATH articles in MSC 30B10https://www.zbmath.org/atom/cc/30B102021-06-15T18:09:00+00:00WerkzeugThe Taylor coefficients of the Jacobi theta constant \(\theta_3\).https://www.zbmath.org/1460.110532021-06-15T18:09:00+00:00"Romik, Dan"https://www.zbmath.org/authors/?q=ai:romik.danSummary: We study the Taylor expansion around the point \(x=1\) of a classical modular form, the Jacobi theta constant \(\theta_3\). This leads naturally to a new sequence \((d(n))_{n=0}^\infty =1,1,-1,51,849,-26199,\dots\) of integers, which arise as the Taylor coefficients in the expansion of a related ``centered'' version of \(\theta_3\). We prove several results about the numbers \(d(n)\) and conjecture that they satisfy the congruence \(d(n)\equiv (-1)^{n-1} (\text{mod }5)\) and other similar congruence relations.Bohr's inequality for harmonic mappings and beyond.https://www.zbmath.org/1460.300032021-06-15T18:09:00+00:00"Kayumova, Anna"https://www.zbmath.org/authors/?q=ai:kayumova.anna"Kayumov, Ilgiz R."https://www.zbmath.org/authors/?q=ai:kayumov.ilgiz-rifatovich"Ponnusamy, Saminathan"https://www.zbmath.org/authors/?q=ai:ponnusamy.saminathanSummary: There has been a number of problems closely connected with the classical Bohr inequality for bounded analytic functions defined on the unit disk centered at the origin. Several extensions, generalizations and modifications of it are established by many researchers and they can be found in the literature, for example, in the multidimensional setting and in the case of the Dirichlet series, functional series, function spaces, etc. In this survey article, we mainly focus on the recent developments on this topic and in particular, we discuss new and sharp improvements on the classical Bohr inequality and on the Bohr inequality for harmonic functions.
For the entire collection see [Zbl 1411.65006].