Documents  11N60 | enregistrements trouvés : 8

Research talks;Dynamical Systems and Ordinary Differential Equations;Number Theory

The Chowla conjecture asserts that the signs of the Liouville function are distributed randomly on the integers. Reinterpreted in the language of ergodic theory this conjecture asserts that the Liouville dynamical system is a Bernoulli system. We prove that ergodicity of the Liouville system implies the Chowla conjecture. Our argument has an ergodic flavor and combines recent results in analytic number theory, finitistic and infinitary decomposition results involving uniformity norms, and equidistribution results on nilmanifolds. The Chowla conjecture asserts that the signs of the Liouville function are distributed randomly on the integers. Reinterpreted in the language of ergodic theory this conjecture asserts that the Liouville dynamical system is a Bernoulli system. We prove that ergodicity of the Liouville system implies the Chowla conjecture. Our argument has an ergodic flavor and combines recent results in analytic number theory, finitistic and infinitary ...

11N60 ; 11B30 ; 11N37 ; 37A45

... Lire [+]

ISBN 978-0-8218-4521-9

Translations of mathematical monographs , 0068

Localisation : Collection 1er étage

theorie des nombres analytique

11-02 ; 11M45 ; 11N60 ; 11Q05

... Lire [+]

- viii; 297 p.
ISBN 978-0-8218-4406-9

CRM proceedings & lecture notes , 0046

Localisation : Collection 1er étage

théorie des nombres # nombre entier # nombre lisse # fonction arithmétique # théorème de Erdös-Kac # polynôme cyclotomique # forme quadratique # fonction zêta # série de Diriclet # L-fonction

11-06 ; 11N25 ; 11N36 ; 11N60 ; 11L07 ; 11L20 ; 11L40 ; 11N37 ; 11N56 ; 11P83

... Lire [+]

- xviii; 414 p.
ISBN 978-0-8218-7577-3

Graduate studies in mathematics , 0134

Localisation : Collection 1er étage

théorie des nombres # algorithme d'Euclide # intégrales # progression arithmétique # treillis # fonction arithmétique # nombre premier # distribution de nombres primaires # conjecture ABC

11A05 ; 11A41 ; 11B05 ; 11K65 ; 11N05 ; 11N13 ; 11N35 ; 11N37 ; 11N60 ; 11B39 ; 11-01 ; 11B25

... Lire [+]

Research talks;Number Theory

Given an additive function $f$ and a multiplicative function $g$, let
$E(f,g;x)=\#\left \{ n\leq x:f(n)=g(n) \right \}$
We study the size of $E(f,g;x)$ for those functions $f$ and $g$ such that $f(n)\neq g(n)$ for at least one value of $n> 1$. In particular, when $f(n)=\omega (n)$ , the number of distinct prime factors of $n$ , we show that for any $\varepsilon >0$ , there exists a multiplicative function $g$ such that
$E(\varepsilon ,g;x)\gg \frac{x}{\left ( \log \log x\right )^{1+\varepsilon }}$,
while we prove that $E(\varepsilon ,g;x)=o(x)$ as $x\rightarrow \infty$ for every multiplicative function $g$. Given an additive function $f$ and a multiplicative function $g$, let
$E(f,g;x)=\#\left \{ n\leq x:f(n)=g(n) \right \}$
We study the size of $E(f,g;x)$ for those functions $f$ and $g$ such that $f(n)\neq g(n)$ for at least one value of $n> 1$. In particular, when $f(n)=\omega (n)$ , the number of distinct prime factors of $n$ , we show that for any $\varepsilon >0$ , there exists a multiplicative function $g$ such that
$E(\varepsilon ...

11N37 ; 11K65 ; 11N60

... Lire [+]

- 100 p.

Localisation : Ouvrage RdC (SQUA)

noyau d'un entier # théorie analytique des nombres

11N25 ; 11N37 ; 11N60

... Lire [+]

- 149 p.

Localisation : Ouvrage RdC (SALD)

séries de Dirichlet # produits eulériens # fonctions multiplicatives # prolongement analytique # distribution limite # transformées de Mellin et de Fourier # fonction Zêta de Riemann # fonction de concentration # crible pondéré

11M41 ; 11N25 ; 11N37 ; 11N60 ; 11N64 ; 30B50 ; 32A99

... Lire [+]