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Superpolynomial convergence in the Riemann Rearrangement Theorem
Stefan Steinerberger
https://arxiv.org/abs/2508.02489 https://arxiv.org/pdf/2508.02489

Superpolynomial convergence in the Riemann Rearrangement Theorem
Let $x \in \mathbb{R}$ be arbitrary and consider the `greedy' approximation of $x$ by signed harmonic sums: given $a_n = \sum_{k \leq n} \varepsilon_k/k$ with $\varepsilon_k \in \left\{-1,1\right\}$, we set $\varepsilon_{n+1} = 1$ if $a_n \leq x$ and $\varepsilon_{n+1} = -1$ otherwise. Bettin-Molteni-Sanna showed (Adv. Math. 2020) that this procedure has remarkable approximation properties: for almost all $x \in \mathbb{R}$ one has superpolynomial convergence in the sense that for every $k \in …

Jährlicher Zubau und Rückbau von #Balkonsolarleistung in Deutschland mit Stand vom 29.08.2025.
Unplausible Inbetriebnahmedaten von 1900 bis 2017 wurden durch das Registrierungsdatum der #Steckersolaranlage ersetzt.
👉 Zusatzlesestoff: Förderantrag

faculty_hiring_us: Faculty hiring networks in the US (2022)
Networks of faculty hiring for all PhD-granting US universities over the decade 2011–2020. Each node is a PhD-granting institution, and a directed edge (i,j) indicates that a person received their PhD from node i and was tenure-track faculty at node j during time of collection (2011-2020). This dataset is divided into separate networks for all 107 fields, as well as aggregate networks for 8 domains, and an overall network for …

SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field
E. Camphuis, W. Quan, L. Balkenhol, A. R. Khalife, F. Ge, F. Guidi, N. Huang, G. P. Lynch, Y. Omori, C. Trendafilova, A. J. Anderson, B. Ansarinejad, M. Archipley, P. S. Barry, K. Benabed, A. N. Bender, B. A. Benson, F. Bianchini, L. E. Bleem, F. R. Bouchet, L. Bryant, M. G. Campitiello, J. E. Carlstrom, C. L. Chang, P. Chaubal, P. M. Chichura, A. Chokshi, T.…

SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field
We present measurements of the temperature and E-mode polarization angular power spectra of the cosmic microwave background (CMB) from observations of 4% of the sky with SPT-3G, the current camera on the South Pole Telescope (SPT). The maps used in this analysis are the deepest used in a CMB TT/TE/EE analysis to date. The maps and resulting power spectra have been validated through blind and unblind tests. The measurements of the lensed EE and TE spectra are the most precise to date at l=1800-4…

Former Raiders First Rounder Called “Worst Draft Pick” https://heavy.com/sports/nfl/las-vegas-raiders/alex-leatherwood-called-worst-draft-pick/?adt_ei=[email]

August 2025 Sees #Newsmax TV Network Finally Agree to Pay $67 Million #Defamation $ettlement To #Dominion #Voting Systems Over Broadcasts Of Nove…