# Search Results

## You are looking at 1 - 6 of 6 items for

• Author or Editor: Michel Weber
• Refine by Access: All Content
Clear All Modify Search

## Divisors, spin sums and the functional equation of the Zeta-Riemann function

Periodica Mathematica Hungarica
Author:
Michel Weber

## Summary

Let \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S_n$ \end{document} , \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $n=1,2\dots$ \end{document} be the sequence of partial sums of independent spin random variables. We show that the distribution value of the divisors of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $S_n$ \end{document} , is intimately related to the Zeta-Riemann function via the functional equation and Theta elliptic functions.

Restricted access

## On a  stronger form  of Salem-Zygmund's inequality for random trigonometric sums with examples

Periodica Mathematica Hungarica
Author:
Michel Weber

## Summary

By applying the majorizing measure method, we obtain a new estimate  of the supremum of random  trigonometric sums. We show that this estimate is strictly stronger than the well-known Salem-Zygmund's estimate, as well as recent general formulations of it obtained by the author. This improvement is obtained by considering the case when the characters are indexed on  sub-exponentially growing sequences of integers. Several remarkable examples are studied.

Restricted access

## Controlling Orthogonal Series with Irrational Rotations

Periodica Mathematica Hungarica
Author:
Michel Weber
Restricted access

## О тождестве Ки Фана

Analysis Mathematica
Author:
Michel Weber

## Abstract

We give several applications of an identity for sums of weakly stationary sequences due to Ky Fan.

Restricted access

## When the cone condition fails

Analysis Mathematica
Author:
Michel Weber
Restricted access

## On the strong law of large numbers and additive functions

Periodica Mathematica Hungarica
Authors:
István Berkes
,
Wolfgang Müller
, and
Michel Weber

## Abstract

Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f, we prove the following weighted strong law of large numbers: if X,X 1,X 2, … is any sequence of integrable i.i.d. random variables, then

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\lim }\limits_{N \to \infty } \frac{{\sum\nolimits_{n = 1}^N {f(n)X_n } }} {{\sum\nolimits_{n = 1}^N {f(n)} }} = \mathbb{E}Xa.s.$$ \end{document}

Restricted access