Hypergeometrie et Fonction Zeta de Riemann cover image. Memoirs of the American Mathematical Society ; 87 pp; Softcover. Request PDF on ResearchGate | Hypergéométrie et fonction zêta de Riemann | Introduction et plan de l’article Arriere plan Les resultats principaux. We provide a lower bound for the dimension of the vector space spanned by 1 and by the values of the Riemann Zeta function at the first odd integers.

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Collection of teaching and learning tools built by Fpnction education experts: L’objectif est alors devenu plus modeste: On prend le logarithme du produit. This value is related to a deep result in renormalization theory Elizalde et al. Many generalizations of the Riemann zeta function, such as Dirichlet seriesDirichlet L -functions and L -functionsare known.

Category:Riemann zeta function

We are using cookies for the best presentation of our site. This fonctiin was subsequently tightened by Zudilinwho showed that at least one of,or is irrational. Rapidly converging series for for odd were first discovered by Ramanujan Zucker, BerndtBailey et al. By using this site, you agree to the Terms of Use and Privacy Policy. This section fomction not cite any sources. An additional set of sums over is given by.


It is related to the Liouville function by. The Theory of the Riemann Zeta-function 2nd ed. Il en existe d’autres. There are a number of similar relations involving various well-known multiplicative functions ; these are given in fpnction article on the Dirichlet series.

Proceedings of the American Mathematical Society. Here, the sum on the right-hand side is exactly the Dirichlet eta function sometimes also called the alternating zeta function. This is ed equality of meromorphic functions valid on the whole complex plane. The Lerch transcendent is given by. There are a number of related zeta functions that can be considered to be generalizations of the Riemann zeta function.

By modifying the contour, Riemann showed that. The study of is significantly more difficult.

On examine ensuite ce qui se passe en 1. Mathematische Zeitschrift in German. An extension of the area of convergence can be obtained by rearranging the original series. OEIS AAand Awhere is a modified Bessel function of the first kindis a regularized hypergeometric function.

Particular values of the Riemann zeta function. Retrieved from ” https: The proof of Euler’s identity uses only the formula for the geometric series and the fundamental theorem of arithmetic. The American Mathematical Monthly. A simpler infinite product expansion is.


Hypergéométrie et fonction zêta de Riemann

T H Seligman and H Nishioka eds. Since holomorphic functions are very general, this property is quite remarkable. Which, when combined with the proof by Lindemann that is transcendental, effectively proves that is transcendental.

Borwein and Bradley; Bailey et al.

Riemann Zeta Function

Multiterm sums for zeha include. En utilisant les formules d’Euler on trouve que: Berlin, Nov. Conference Proceedings, Canadian Mathematical Society.

Two surprising sums involving are given by.

An Introduction to the Bosonic String. Algebra, The first proof of universality was provided by Sergei Mikhailovitch Voronin in Rivoal and Ball and Rivoal proved that there are infinitely many integers such that is irrational, and subsequently that at least one of, Princeton University Press, The Riemann hypothesis would imply that this proportion is 1.

Pour l’avant-dernier terme on a. How Euler Did It.