Results 11 to 20 of about 5,228,205 (65)
Moments of the Dedekind zeta function [PDF]
, 2013 We study analytic aspects of the Dedekind zeta function of a Galois extension. Specifically, we are interested in its mean values. In the first part of this thesis we give a formula for the second moment of the Dedekind zeta function of a quadratic ...
Heap, Winston
core +6 more sources
On Evaluation of Riemann Zeta function ζ(s) [PDF]
, 2002 In this paper, by using Fourier series theory, several summing formulae for Riemann Zeta function ζ(s) and Dirichlet series are ...
Qi, Feng, Luo, Qiu-Ming, Guo, Bai-Ni
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On zero-density estimates for Beurling zeta functions [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZEWe show the zero-density estimate \[ N(ζ_{\mathcal{P}}; α, T) \ll T^{\frac{4(1-α)}{3-2α-θ}}(\log T)^{9} \] for Beurling zeta functions $ζ_{\mathcal{P}}$ attached to Beurling generalized number systems with integers distributed as $N_{\mathcal{P}}(x) = Ax + O(x^θ)$.
Broucke, Frederik
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Limit laws for rational continued fractions and value distribution of quantum modular forms
Proceedings of the London Mathematical Society, Volume 125, Issue 6, Page 1377-1425, December 2022., 2022 Abstract We study the limiting distributions of Birkhoff sums of a large class of cost functions (observables) evaluated along orbits, under the Gauss map, of rational numbers in (0, 1] ordered by denominators. We show convergence to a stable law in a general setting, by proving an estimate with power‐saving error term for the associated characteristic
Sandro Bettin, Sary Drappeau
wiley +1 more source
Totally null sets and capacity in Dirichlet type spaces
Journal of the London Mathematical Society, Volume 106, Issue 3, Page 2030-2049, October 2022., 2022 Abstract In the context of Dirichlet type spaces on the unit ball of Cd$\mathbb {C}^d$, also known as Hardy–Sobolev or Besov–Sobolev spaces, we compare two notions of smallness for compact subsets of the unit sphere. We show that the functional analytic notion of being totally null agrees with the potential theoretic notion of having capacity zero.
Nikolaos Chalmoukis, Michael Hartz
wiley +1 more source
Exterior products of operators and superoptimal analytic approximation
Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 299-412, December 2021., 2021 Abstract We give a new algorithm for the construction of the unique superoptimal analytic approximant of a given continuous matrix‐valued function on the unit circle, using exterior powers of operators in preference to spectral or Wiener–Masani factorizations.
Dimitrios Chiotis +2 more
wiley +1 more source
The holomorphic flow of the Riemann zeta function [PDF]
, 2003 The flow of the Riemann zeta function, ś = ς(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line.
Barnett, A. Ross, Broughan, Kevin A.
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Toeplitz Operators whose Symbols Are Borel Measures
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 In this paper, we are concerned with Toeplitz operators whose symbols are complex Borel measures. When a complex Borel measure μ on the unit circle is given, we give a formal definition of a Toeplitz operator Tμ with symbol μ, as an unbounded linear operator on the Hardy space. We then study various properties of Tμ. Among them, there is a theorem that
Jaehui Park, Chun Lu
wiley +1 more source
Products of Toeplitz Operators on the 2‐Analytic Bergman Space
Journal of Function Spaces, Volume 2021, Issue 1, 2021., 2021 Let f and g be bounded functions, and let Tf and Tg be Toeplitz operators on A22D. We show that if the product TfTg equals zero and one of f and g is a radial function satisfying a Mellin transform condition, then the other function must be zero.
Bo Zhang +3 more
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Peak sets and boundary interpolation sets for the unit disc: a survey
Bulletin of the London Mathematical Society, Volume 52, Issue 6, Page 993-1009, December 2020., 2020 Abstract This paper surveys results concerning peak sets and boundary interpolation sets for the unit disc. It includes hitherto unpublished results proved by Ullrich on peak sets for the Zygmund class.
Alan Noell
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