Analysis on arithmetic schemes. I.
Analytic and arithmetic theory of semigroups with divisor theory
Analytic and combinatoric aspects of Hurwitz polyzêtas
In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the...
Analytic Class Number Formulas in Function Fields.
Analytic continuation of multiple zeta-functions and their values at non-positive integers
Analytic continuation of partial zeta functions of arithmetic orders.
Analytic continuation of representations and estimates of automorphic forms.
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan.
Analytic Erdős-Turán conjectures and Erdős-Fuchs theorem.
Analytic formulas for the regulator of a number field.
Analytic normal basis theorem
Let p be a prime number, ℚp the field of p-adic numbers, and a fixed algebraic closure of ℚp. We provide an analytic version of the normal basis theorem which holds for normal extensions of intermediate fields ℚp ⊆ K ⊆ L ⊆ .
Analytic number theory in formations based on additive arithmetical semigroups.
Analytic potential theory over the -adics
Over a non-archimedean local field the absolute value, raised to any positive power , is a negative definite function and generates (the analogue of) the symmetric stable process. For , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.
Analytic properties of zeta functions and subgroup growth.
Analytic Subgroups of Group Varieties.
Analytic torsions on contact manifolds
We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any -dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable...
Analytical construction of Weil curves over function fields
Andrianov' s L-functions associated to Siegel wave forms of degree two.
Angular distribution of units in abelian group rings - an application to Galois-module theory.
Anisotropic forms modulo p²