... НЕПРЕРЫВНОГО МАТЕМАТИЧЕСКОГО ОБРАЗОВАНИЯ . ... Кружок ?Олимпиады и математика? ... Московская математическая олимпиада . Заочный математический конкурс . ... Устные математические олимпиады . Олимпиады по программированию . Математический праздник . Математические регаты . ... Математические бои . Олимпиада по геометрии им. И.Ф.Шарыгина . ... Программа ?Math in Moscow? Научные конкурсы . Творческий конкурс . ... График олимпиад . ... XXVII Математический праздник . ...
Some Hilbert spaces of square integrable functions on the positive half-line arise naturally (via the "co-Poisson" formula) in the study of the Riemann, Dirichlet or Dedekind zeta functions. ... Among these families of Hilbert spaces, one has been established to be intimately associated with the Klein-Gordon equation in 1+1 dimensions and especially with the Einstein causality property of this hyperbolic equation (for a classical field). ... Site design by Paul Zinn-Justin (2005) ...
In the first part of this talk, I will give a very short survey of the theory of zeta functions associated to polynomials of several variables and its applications in Number theory, Arithmetic geometry, etc.. In the second part of this talk, I will give a new method which allows studying analytical properties of zeta functions associated to a class of arithmetical functions mixing additive and multiplicative data. I will also give two applications. ...
In this talk I give an introduction to generalizations of the Riemann zeta function called "Weyl group multiple Dirichlet series". Weyl group multiple Dirichlet series are sums in several variables whose coefficients involve Gauss sums and also reflect the combinatorics of a given root system. ... These functions and their residues unify and generalize a number of examples which have been previously treated individually, often with applications to number theory. ...
Riemann's zeta-function satisfies a convexity bound on the critical line; moreover, $\zeta(s)$ is non-vanishing in a neighborhood of the edge of the critical strip. Let $L(s,\pi,r)$ be a Langlands-Shahidi L-function; what generalizations of $\zeta(s)$ can be said about this $L(s,\pi,r)$? Does it satisfy a convexity bound on the critical line? Is it non-vanishing close to the edge of the critical strip? ...
... The zeta function of the classical monodromy transformation of the germ $f$ is a topological invariant of it. Let us consider a parametrization (uniformization) of the curve $(C,0)$. The order of a function on $(C,0)$ as a function in the uniformization parameter defines a decreasing filtration on the ring of functions on the curve singularity. It appears that the Poincare series of this filtration (considered as a rational function) coincides with the zeta function mentioned above. ...
. This talk is a continuation of Sol Friedberg's talk. I'll present a survey of some of the applications and potential applications of multiple Dirichlet series to non-vanishing results and moments of zeta functions and L-series. Go to the Laboratoire Poncelet home page. Site design by Paul Zinn-Justin (2005)
... Fix $s$ with $Re (s)=\sigma$, and let $\chi$ run over all Dirichlet characters with (say) prime conductors. Then (generally conjecturally), $M_{\sigma}(z)$ (resp. $\tilde{M}_{\sigma}(z)$) coincides with the limit-average over $\chi$ of $\delta_z(L'(\chi,s)/L(\chi,s))$ (resp. $\psi_z(L'(\chi,s)/L(\chi,s))$). Here $\delta_z(w)$ is the Dirac measure concentrated at $z$ and $\psi_z(w)=\exp(i Re(\bar{z}w))$ is the additive character on the field of complex numbers parametrized by $z$. ...
In the main part of this lecture, we will give an overview of the theory of fractal strings and of the associated complex fractal dimensions, with emphasis on the case of self-similar strings. ... These oscillations are expressed in terms of suitable explicit formulas (in the sense of number theory, but more general) and yield precise asymptotic expansions for certain geometric, dynamical or spectral counting functions associated to fractal strings. ...
In the report, we will discuss the value distribution of the modified Mellin transform of the square of the Riemann zeta-function introduced and studied by A.Ivic, M.Jutila and Y.Motohashi. We will recall its analytical properties as well as some estimates and mean square estimates. After this, we will state continuous and discrete limit theorems in the sense of weak convergence of probability measures on the complex plane and in the space of meromorphic functions for this transform. ...
The Tsfasman-Vladuts' generalized Brauer Siegel Theorem gives us the asymptotic behaviour of the residue of zeta at $s=1$ in a tower of fields. It's closely related to Mertens theorem which can be seen as the finite step of Brauer-Siegel theorem in the case of $\mathbb{Q}$. Mireille Car generalized it in the case of function fields, but it can also be generalized in the case of any global fields, and this leads to an explicite version of B-S theorem under GRH. ...
. We find an explicit solution in Shimura's conjecture for Sp3 (1963). The existence of the solution was established for any genus n by A.N.Andrianov. We develop formulas for the Satake spherical maps for Sp_n and Gl_n. Go to the Laboratoire Poncelet home page. Site design by Paul Zinn-Justin (2005)
The Riemann xi-function is an entire function of order one and its zeroes coincide with non-trivial zeroes of the Riemann zeta-function which lie in the critical strip. The Riemann hypothesis asserts that all zeroes of the Riemann xi-function lie on the critical line. ... Moreover, if the Riemann hypothesis is fulfilled, then all zeroes of derivatives of the Riemann xi-function lie on the critical line. ...