Ludovic Delabarre
Multivariable analogue of the conjecture of Z. Rudnick and M. du Sautoy and application to a problem of N. Kurokawa and H. Ochiai.
Пнд, 04/05/2010 - 15:01 — SomNambulAuthors: Ludovic Delabarre
Subjects: Number Theory
AbstractThis work introduces a multivariable analogue of a conjecture of Z. Rudnick
and M. du Sautoy concerning the maximal domain of meromorphy of uniform
eulerian products. In particular we apply methods which have been introduced in
a previous article to resolve a problem of N. Kurokawa and H. Ochiai concerning
the natural boundary of meromorphy of Igusa's multivariable zeta function
$Z^{\textrm{ring}}(s_1,...,s_n; \mathbf{Z}[T,T^{-1}])$.Extension of Estermann's theorem to eulerian products associated to a multivariate polynomial.
Пт, 01/22/2010 - 16:01 — SomNambulAuthors: Ludovic Delabarre
Subjects: Number Theory
AbstractGiven a multivariate polynomial $h(X_1,...,X_n)$ with integral coefficients,
we determine the maximal domain of meromorphy of the eulerian product
$\prod_{p}h(p^{-s_1},...,p^{-s_n})$. The polynomials whose associated eulerian
product extends to $\mathbf{C}^n$ are completely characterised and furthermore
the natural boundary is explained when it exists. So we generalise a theorem
for one variable polynomials due to Estermann. As an application, we explicit
the natural boundary of the multivariate eulerian product associated to a toric
variety $X$.
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