All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 72

Showing per page

Singularité de séries de Dirichlet associées à des polynômes de plusieurs variables et applications en théorie analytique des nombres

Driss Essouabri (1997)

Annales de l'institut Fourier

Soit P ∈ ℝ [ X 1 , ... , X n ] un polynôme. On appelle série de Dirichlet associée à P la fonction : s ↦ Z ( P ; s ) = ∑ m ∈ ℕ * n P ( m ) - s ( s ∈ ℂ ) . Dans cet article nous étudions l’existence et les propriétés du prolongement méromorphe d’une telle série sous l’hypothèse qu’il existe B ∈ ] 0 , 1 [ tel que : i) P ( x ) → + ∞ quand | | x | | → + ∞ et x ∈ [ B , + ∞ [ n et ii) d ( Z ( P ) , [ B , + ∞ [ n ) > 0 où Z ( P ) = { z ∈ ℂ n | P ( z ) = 0 } . Cette hypothèse est probablement optimale et en tout cas contient strictement toutes les classes de polynômes déjà traitées antérieurement. Sous cette hypothèse nos principaux résultats sont : l’existence du prolongement méromorphe au plan...

Small values of the Riemann zeta function on the critical line

Justas Kalpokas, Paulius Šarka (2015)

Acta Arithmetica

We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.

Solution to a problem of Bombieri

Andrew Granville (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We solve a problem of Bombieri, stated in connection with the «prime number theorem» for function fields.

Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions

James Haglund (2011)

Open Mathematics

Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show how this...

Some infinite sums identities

Meher Jaban, Sinha Sneh Bala (2015)

Czechoslovak Mathematical Journal

We find the sum of series of the form ∑ i = 1 ∞ f ( i ) i r for some special functions f . The above series is a generalization of the Riemann zeta function. In particular, we take f as some values of Hurwitz zeta functions, harmonic numbers, and combination of both. These generalize some of the results given in Mező’s paper (2013). We use multiple zeta theory to prove all results. The series sums we have obtained are in terms of Bernoulli numbers and powers of π .

Some problems on mean values of the Riemann zeta-function

Aleksandar Ivić (1996)

Journal de théorie des nombres de Bordeaux

Several problems and results on mean values of ζ ( s ) are discussed. These include mean values of | ζ ( 1 2 + i t ) | and the fourth moment of | ζ ( σ + i t ) | for 1 / 2 < σ < 1 .

Currently displaying 21 – 40 of 72