The thesis also looks briefly at the history of the subject of the irrationality of naturally occurring numbers in mathematics. The crux of all the proofs is the same and this is examined in detail.;The first proof that zeta (3) is irrational is taken from Van der Poorten's informal ...
The Zeta Quotient $ζ(3)/ π^3$ is Irrational This note proves that the first odd zeta value does not have a closed form\nformula $\\zeta(3)e r \\pi^3$ for any rational number $r \\in \\mathbb{Q}$.\nFurthermore, assuming the irrationality of the second odd zeta value\n$\...
so there is nothing more about their zeros. For rational values of a other than 1/2 or 1 or for transcendental values of a, it is known that ζ(z, a) has an infinity of zeros with Re z > 1. For irrational algebraic values of a it is not known whether there are any zeros with...
This note proves that the first odd zeta value does not have a closed form\nformula $\\zeta(3)e r \\pi^3$ for any rational number $r \\in \\mathbb{Q}$.\nFurthermore, assuming the irrationality of the second odd zeta value\n$\\zeta(5)$, it is shown that $\\zeta(5)e r\...
One of the Eight Numbers \\zeta(5),\\zeta(7),\\dots,\\zeta(17),\\zeta(19) Is IrrationalRiemann zeta-functionirrationality of values of the zeta-functionNikishin--Rivoal arithmetical schemeZudilin V.Vmathematical notes
Macaitienė, Value distribution of the Lerch zeta-function with algebraic irrational parameter. III, Lith. Math. J. , 48 (3):282–293, 2008.Garbaliauskienė, V, Genienė, D, Laurinčikas, A (2007) Value distribution of the Lerch zeta-function with algebraic irrational parameter. I...
We obtain a limit theorem in the sense of weak convergence of probability measures in the space of analytic functions for the Lerch zeta-function with algebraic irrational parameter.Danute GenieneAntanas LaurincikasRenata MacaitieneLithuanian mathematical journal...
Zudilin, W. "One of the Numbers , , , Is Irrational." Uspekhi Mat. Nauk 56, 149-150, 2001.Zvengrowski, P. and Saidak, F. "On the Modulus of the Riemann Zeta Function in the Critical Strip." Math. Slovaca 53, 145-172, 2003....
is (sqrt(8)-sqrt(2))^2 irrational?ReferencesBombieri, E. and Lagarias, J. C. "Complements to Li's Criterion for the Riemann Hypothesis." J. Number Th. 77, 274-287, 1999.Brent, R. P. "On the Zeros of the Riemann Zeta Function in the Critical Strip." Math. Comput. 33, 1361-...