Concept

Quotient group

Related publications (30)

A new elementary proof of the Prime Number Theorem

Let

\Omega(n)

denote the number of prime factors of

n

. We show that for any bounded

f\colon\mathbb{N}\to\mathbb{C}

one has [ \frac{1}{N}\sum_{n=1}^N, f(\Omega(n)+1)=\frac{1}{N}\sum_{n=1}^N, f(\Omega(n))+\mathrm{o}_{N\to\infty}(1). ] This yields a ...

2021

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Florian Karl Richter

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...

2020

Multiplicative combinatorial properties of return time sets in minimal dynamical systems

Florian Karl Richter

We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove t ...

2019

A generalization of Kátai's orthogonality criterion with applications

Florian Karl Richter

We study properties of arithmetic sets coming from multiplicative number theory and obtain applications in the theory of uniform distribution and ergodic theory. Our main theorem is a generalization of Kátai's orthogonality cri ...

2019

Observation of the $\chi_\mathrm{b1}$(3P) and $\chi_\mathrm{b2}$(3P) and measurement of their masses

Jian Wang, Matthias Finger, Lesya Shchutska, Qian Wang, Yiming Li, Matthias Wolf, Varun Sharma, Konstantin Androsov, Jan Steggemann, Leonardo Cristella, Xin Chen, Davide Di Croce, Mingkui Wang, Zhirui Xu, Chao Wang, João Miguel das Neves Duarte, Tagir Aushev, Tian Cheng, Yixing Chen, Werner Lustermann, Andromachi Tsirou, Alexis Kalogeropoulos, Andrea Rizzi, Ioannis Papadopoulos, Paolo Ronchese, Thomas Muller, Ho Ling Li, Giuseppe Codispoti, Hua Zhang, Siyuan Wang, Peter Hansen, Daniel Gonzalez, Tao Huang, David Vannerom, Michele Bianco, Kun Shi, Wei Shi, Abhisek Datta, Ji Hyun Kim, Donghyun Kim, Dipanwita Dutta, Zheng Wang, Sanjeev Kumar, Wei Li, Yong Yang, Yi Wang, Ajay Kumar, Ashish Sharma, Georgios Anagnostou, Joao Varela, Csaba Hajdu, Muhammad Ahmad, Ekaterina Kuznetsova, Ioannis Evangelou, Matthias Weber, Muhammad Shoaib, Milos Dordevic, Vineet Kumar, Vladimir Petrov, Francesco Fiori, Quentin Python, Meng Xiao, Hao Liu, Sourav Sen, Viktor Khristenko, Marco Trovato, Gurpreet Singh, Fan Xia, Xiao Wang, Bibhuprasad Mahakud, Jing Li, Rajat Gupta, Lei Feng, Muhammad Waqas, Hui Wang, Seungkyu Ha, Davide Cieri, Maren Tabea Meinhard, Giorgia Rauco, Ali Harb, Benjamin William Allen, Pratyush Das, Miao Hu, Lei Li

The

\chi_\mathrm{b1}

(3P) and

\chi_\mathrm{b2}

(3P) states are observed through their

\Upsilon

(3S)

\gamma

decays, using an event sample of proton-proton collisions collected by the CMS experiment at the CERN LHC. The data were collected at a center-o ...

2018

Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs

We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation, and an Anion-style transformation is applied using this operation. It is shown that as the number of pola ...

2018

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

A Householder-Based Algorithm For Hessenberg-Triangular Reduction

Daniel Kressner, Zvonimir Bujanovic

The QZ algorithm for computing eigenvalues and eigenvectors of a matrix pencil A - lambda B requires that the matrices first be reduced to Hessenberg-triangular (HT) form. The current method of choice for HT reduction relies entirely on Givens rotations re ...

SIAM PUBLICATIONS2018

Dependence of the L-Mode scrape-off layer power fall-off length on the upper triangularity in TCV

Stefano Coda, Holger Reimerdes, Benoît Labit, Christian Gabriel Theiler, Antoine Pierre Emmanuel Alexis Merle, Roberto Maurizio, Bernhard Sieglin

This paper reports on experimental observations on TCV with a scan in upper triangularity

{\delta }_{\mathrm{up}}

, including negative triangularity, focusing on the power fall-off length

{\lambda }_{{\rm{q}}}

in L-Mode. The upper triangularity is scann ...

2018

Polarization and Channel Ordering: Characterizations and Topological Structures

Rajai Nasser

Information theory is the field in which we study the fundamental limitations of communication. Shannon proved in 1948 that there exists a maximum rate, called capacity, at which we can reliably communicate information through a given channel. However, Sha ...

EPFL2017

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