Documents  11M26 | enregistrements trouvés : 40

- 234 p.
ISBN 978-0-8218-3136-6

Proceedings of the Steklov institute of mathematics , 0189

Localisation : Collection 1er étage

fonctions # théorie des fonctions

11M26 ; 41A05 ; 41A10 ; 41A15 ; 41A35

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Localisation : Colloque 1er étage (MAIO)

conjecture de Goldbach # fonction zeta de Riemann # problème de Goldbach # produit de Euler # théorie analytique des nombres

11M26 ; 11M41 ; 11Mxx ; 11P32 ; 11R42

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- 382 p.
ISBN 978-0-521-62512-8

London mathematical society lecture note series , 0247

Localisation : Collection 1er étage

complexité analytique # distribution # décomposition # fonction zeta # forme modulaire # formule de trace de Kuznetsov # série de Dirichlet # théorie des nombres analytique

11F11 ; 11F66 ; 11Fxx ; 11M06 ; 11M26

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- xi; 329 p.
ISBN 978-0-8218-9173-5

CRM proceedings & lecture notes , 0055

Localisation : Collection 1er étage

théorie du potentiel # fonction d'une variable complexe

30-XX ; 31-XX ; 32-XX ; 00B25 ; 30-06 ; 31-06 ; 32-06 ; 11M26 ; 60J45 ; 53A10 ; 35N15 ; 44A15

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- x; 319 p.
ISBN 978-1-4614-5340-6

Fields institute communications , 0065

Localisation : Collections RdC

produit de Blaschke # espace de Hardy # théorie des opérateurs # système dynamique # analyse harmonique # EDP

30D50 ; 30D40 ; 30D55 ; 30E20 ; 30E25 ; 32A36 ; 30-06 ; 47-06 ; 47B35 ; 11M26 ; 00B25

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- viii; 399 p.
ISBN 978-0-8218-9147-6

Contemporary mathematics , 0600

Localisation : Collection 1er étage

Benoît Mandelbrot # fractales # systèmes dynamiques

28A12 ; 28A78 ; 28A80 ; 11M26 ; 11M41 ; 37A45 ; 37C45 ; 37F10 ; 58B20 ; 58C40 ; 00B25 ; 28-06 ; 11-06 ; 37-06 ; 58-06

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Number Theory

Fermat showed that every prime $p = 1$ mod $4$ is a sum of two squares: $p = a^2 + b^2$, and hence such a prime gives rise to an angle whose tangent is the ratio $b/a$. Hecke showed, in 1919, that these angles are uniformly distributed, and uniform distribution in somewhat short arcs was given in by Kubilius in 1950 and refined since then. I will discuss the statistics of these angles on fine scales and present a conjecture, motivated by a random matrix model and by function field considerations. Fermat showed that every prime $p = 1$ mod $4$ is a sum of two squares: $p = a^2 + b^2$, and hence such a prime gives rise to an angle whose tangent is the ratio $b/a$. Hecke showed, in 1919, that these angles are uniformly distributed, and uniform distribution in somewhat short arcs was given in by Kubilius in 1950 and refined since then. I will discuss the statistics of these angles on fine scales and present a conjecture, motivated by a ...

11M26 ; 11M06 ; 11F66 ; 11T55 ; 11R44 ; 11M50

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History of Mathematics;Probability and Statistics;Number Theory

One fairly standard version of the Riemann Hypothesis (RH) is that a specific probability density on the real line has a moment generating function (Laplace transform) that as an analytic function on the complex plane has all its zeros pure imaginary. We’ll review a series of results that span the period from the 1920’s to 2018 concerning a perturbed version of the RH. In that perturbed version, due to Polya, the log of the probability density is modified by a kind of mass term (in quantum field theory language). This gives rise to an implicitly defined real constant known as the de Bruijn-Newman Constant, Lambda. The conjecture and now theorem (Newman 1976, Rodgers and Tau 2018) that Lambda is greater than or equal to zero is complementary to the RH which is equivalent to Lambda less than or equal to zero; The conjecture/theorem is a version of the dictum that the RH, if true, is only barely so. We’ll also briefly discuss some connections with quantum field theory and the Lee-Yang circle theorem. One fairly standard version of the Riemann Hypothesis (RH) is that a specific probability density on the real line has a moment generating function (Laplace transform) that as an analytic function on the complex plane has all its zeros pure imaginary. We’ll review a series of results that span the period from the 1920’s to 2018 concerning a perturbed version of the RH. In that perturbed version, due to Polya, the log of the probability density ...

11M26 ; 60K35

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Mathematical Physics;Probability and Statistics

For 20 years we have known that average values of characteristic polynomials of random unitary matrices provide a good model for moments of the Riemann zeta function. Now we consider mixed moments of characteristic polynomials and their derivatives, calculations which are motivated by questions on the distribution of zeros of the derivative of the Riemann zeta function.

15B52 ; 11M26 ; 11M06

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- 412 p.
ISBN 978-0-19-853369-6

Oxford science publications

Localisation : Ouvrage RdC (TITC)

fonction zeta de Riemann

11M26 ; 11Mxx

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- pag. mult.

I.h.e.s./m/79/305

Localisation : Ouvrage RdC (CART)

fonction zeta de Selberg

11F67 ; 11F72 ; 11M26 ; 11M41

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- 156 p.
ISBN 978-0-521-33535-5

Cambridge studies in advanced mathematics , 0014

Localisation : Ouvrage RdC (PATT)

fonction zéta de Riemann

10H05 ; 11M26

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Localisation : Oeuvres complètes RdC (BOHR)

Bohr # série de Dirichlet # zeta-fonction de Riemann # oeuvres complètes

01A60 ; 01A75 ; 11F66 ; 11M26 ; 30B50

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- 396 p.
ISBN 978-3-11-013170-3

De Gruyter expositions in mathematics , 0005

Localisation : Ouvrage RdC (KARA)

distribution des premiers # fonction zeta de Riemann # somme de Weyl # théorie des nombres # théorie des nombres multiplicatifs

11-02 ; 11L15 ; 11M06 ; 11M26 ; 11N05

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- 524 p.
ISBN 978-3-540-62745-6

Springer monographs in mathematics

Localisation : Ouvrage RdC (ELST)

PSL(2,O) # action de groupe # entier quadratique imaginaire # espace hyperbolique # factorisation de Hadamard # fonction automorphe # fonction zeta # forme automorphe # forme bilinéaire # forme et groupe algébrique linéaire # forme hermitienne d'intégrale binaire # groupe de Coxeter # groupe discontinu # groupe uni-modulaire # operateur de Laplace # série de Eisenstein # théorie des nombres # théorème géodésique

11E39 ; 11E45 ; 11F55 ; 11F72 ; 11M26

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- 268 p.
ISBN 978-0-8176-4098-9

Localisation : Ouvrage RdC (LAPI)

théorie des nombres # fonction zeta # fractale # corde fractale # dimension complexe # géométrie spectrale # zéro de la fonction zeta # oscillation

11M26 ; 11M41 ; 28A75 ; 28A80 ; 35P20 ; 58G25

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- 193 p.
ISBN 978-2-7302-1011-9

Localisation : Ouvrage RdC (Fonc)

fonction zeta # arithmétique # théorème des nombres premiers # transformation de Fourier # forme modulaire # fonction zeta de Riemann # propriété diophantienne # variable p-adique # fonction zeta p-adique # probabilité

11Mxx ; 11M26 ; 11Fxx

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- 422 p.
ISBN 978-0-309-08549-6

Localisation : Ouvrage RdC (DERB)

théorie des nombres # histoire des mathématiques # 19ème siècle # nombre premier # hypothèse de Riemann # série

11-01 ; 11-03 ; 01A55 ; 11M26 ; 11N05

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- 460 p.
ISBN 978-0-387-33285-5

Springer monographs in mathematics

Localisation : Ouvrage RdC (LAPI)

fractale # mesure géométrique # fonction zéta # spectre d'anneau fractale # chaine fractale généralisé # hypothèse de Riemann # théorie de Nevanlinna # zéro de fonction zéta

11M26 ; 11M41 ; 28A75 ; 28A80 ; 35P20 ; 58G25

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