Laboratoire J.-V. Poncelet
Universite de Caen, France
On a class of (mixed) zeta functions and applications
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. First, I will explain how this proves Manin's conjecture for a class of rational projective toric varieties with a large class of heights other than the usual one that comes from the standard metric on projective space. As a second application, I will give a general result on the representation of integers by polynomials evaluated at integer points subject to conditions typically enjoyed by arithmetic functions.
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