Gauthier, Paul M
- Professeur associé
-
Faculté des arts et des sciences - Département de mathématiques et de statistique
André-Aisenstadt Local 4145
Courriels
Affiliations
- Membre Centre de recherches mathématiques
- Membre CRM Centre de recherches mathématiques
Expertise
J'ai fait de la recherche en analyse complexe et en théorie du potentiel - surtout l'approximation par fonctions holomorphes ou harmoniques. Depuis quelques années, je rode autour de l'hypothèse de Riemann en utilisant des méthodes d'approximation complexe plutôt que de la théorie des nombres.
Pour toutes mes publications, voir mathscinet
Projets de recherche Tout déplier Tout replier
Centre de recherches mathématiques (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2022 - 2029
Complex approximation on Riemann surfaces and in infinite dimensions CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016 - 2025
Complex approximation on Riemann surfaces and in infinite dimensions CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016 - 2024
Complex approximation on Riemann surfaces and in infinite dimensions CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016 - 2023
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2015 - 2023
CENTRE DE RECHERCHES MATHEMATIQUES (CRM) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2008 - 2016
ANALYTIC APPROXIMATION CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 1994 - 2015
Publications choisies Tout déplier Tout replier
Mergelyan's theorem with polynomials non-vanishing on unions of sets
Universally overconvergent power series via the Riemann zeta-function
On the instability of the Riemann hypothesis for curves over finite fields
Approximating functions by the Riemann zeta-function and by polynomials with zero constraints
Domains of injective holomorphy
Zero-free polynomial approximation on a chain of Jordan domains
$C^m$-subharmonic extension of Runge type from closed to open subsets of $\Bbb R^N$
Approximating all meromorphic functions by linear motions of the Riemann zeta-function
On the instability of the Riemann hypothesis for varieties over finite fields
Traces of entire functions on algebraic subvarieties
The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings
Approximation of and by the Riemann zeta-function
Hartogs' theorem on separate holomorphicity for projective spaces
Composition operators on $\mu$-Bloch spaces
Rational approximation and universality for a quasilinear parabolic equation
The FLRW cosmological model revisited: relation of the local time with the local curvature and consequences on the Heisenberg uncertainty principle
Value distribution of the Riemann zeta function
Approximation by translates of Taylor polynomials of the Riemann zeta function
Boundedness from below of composition operators on $\alpha$-Bloch spaces
Universal (pluri)subharmonic functions
Universal overconvergence of homogeneous expansions of harmonic functions
Embedding Stein manifolds and tangential approximation
Approximation by rational mappings, via homotopy theory
Simultaneous approximation on two subsets of an open Riemann surface
Covering properties of most entire functions on Stein manifolds
The existence of universal inner functions on the unit ball of $\Bbb C^n$
Alice in Switzerland: the life and mathematics of Alice Roth
Approximation by the Riemann zeta-function
Small perturbations of the Riemann zeta function and their zeros
On uniform approximation by $n$-analytic functions on closed sets in $\Bbb C$
Harmonic approximation on compact sets
Cercles de remplissage for the Riemann zeta function
Approximation on closed sets by analytic or meromorphic solutions of elliptic equations and applications
BiBloch-type maps: existence and beyond
Approximation on arcs and dendrites going to infinity in $\Bbb C^n$
Tangential approximation and universality
Approximation by meromorphic functions with Mittag-Leffler type constraints
Bloch constants in several variables
Bloch constants for planar harmonic mappings
Functions of bounded expansion: normal and Bloch functions
Carleman approximation on products of Riemann surfaces
Note on the support of Sobolev functions
Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds
Normal functions: $L^p$ estimates
On Bloch's constant
On strongly normal functions
Recent developments in harmonic approximation, with applications
Propagation of smallness and the uniqueness of harmonic and holomorphic functions
Superharmonic approximation on a closed set
Fusion of two solutions of a partial differential equation
Subharmonic extensions and approximations
Best uniform approximation by harmonic functions on subsets of Riemannian manifolds
Best uniform approximation by solutions of elliptic differential equations
Approximation by harmonic functions in $C^1$-norm, and the harmonic $C^1$-width of compact sets in ${\bf R}^n$
Harmonic approximation on arcs
Degenerate cases of uniform approximation by solutions of systems with surjective symbols
Uniform approximation and fine potential theory
Approximation by (pluri)subharmonic functions: fusion and localization
A maximum principle for subharmonic and plurisubharmonic functions
Polynomial approximation on certain Lipschitz graphs in ${\bf C}^n$
An arc of finite $2$-measure that is not rationally convex
Global holomorphic approximation on the product of curves in ${\bf C}^n$
A problem of Rubel concerning approximation on unbounded sets by entire functions
Approximation of a function and its derivatives by entire functions of several variables
Approximation by harmonic functions on closed subsets of Riemann surfaces
Asymptotic maximum principles for subharmonic and plurisubharmonic functions
Approximation uniforme par des fonctions harmoniques avec singularités
Uniform approximation on closed sets by solutions of elliptic partial differential equations
Global holomorphic approximations of CR functions on CR manifolds
Some properties of Baouendi-Trèves type approximations of Cauchy-Riemann functions
Note on the decay of solutions of elliptic equations
Remarks on a theorem of Keldysh and Lavrent'ev
Approximation harmonique sur les surfaces de Riemann
Uniform approximation on closed sets by harmonic functions with Newtonian singularities
On tangential approximation by holomorphic functions
Approximation harmonique, approximation holomorphe et topologie
Approximation uniforme qualitative sur des ensembles non bornés
Uniform approximation on unbounded sets by harmonic functions with logarithmic singularities
Approximation uniforme sur des parties non bornées par des fonctions essentiellement harmoniques
Complex approximation and simultaneous interpolation on closed sets
From local to global properties of subharmonic functions on Green spaces
Holomorphic functionals on open Riemann surfaces
Possibility of uniform rational approximation in the spherical metric
The distribution of cercles de remplissage for functions having spiral asymptotic values
The set of Julia points for functions omitting two values
Asymptotic values along Julia rays
Possibility of complex asymptotic approximation on closed sets
Équidistribution des valeurs d'une application holomorphe générique à valeurs dans l'espace projectif
Interpolation in separable Fréchet spaces with applications to spaces of analytic functions
Most power series have radius of convergence $0$ or $1$
Continuous boundary behaviour for functions defined in the open unit disc
Équidistribution des valeurs d'une fonction analytique générique sur un espace de Stein
Complex approximation for vector-valued functions with an application to boundary behaviour
Problème de surjectivité des applications holomorphes
Approximation sur les fermés par des fonctions analytiques sur une surface de Riemann
Local harmonic majorants of functions subharmonic in the unit disc
The local range set of a meromorphic function
The value distribution of most functions of one or several complex variables
Some applications of Arakélian's approximation theorems to the theory of cluster sets
Behavior of normal meromorphic functions on the maximal ideal space of $H^{\infty }$
The range set of a meromorphic function---A topological approach
Unbounded holomorphic functions bounded on a spiral
The maximum modulus of normal meromorphic functions and applications to value distribution
Cercles de remplissage and asymptotic behaviour along circuitous paths
Tangential approximation by entire functions and functions holomorphic in a disc
Cluster sets on a Banach algebra of non-tangential curves
Cercles de remplissage and asymptotic behaviour
The non-Plessner points for the Schwarz triangle functions
A criterion for normalcy