Grant: Canada Research Chairs
Université de Montréal
$200,000.00
number theory
EF 2023-24
Résumé
The principal investigator is developing an alternative approach to analytic number theory, the first coherent program since Riemann's 1859 memoir. He can now reprove all classical results, quantitatively and qualitatively, providing simpler proofs of notoriously difficult results (E.g Theorems of Linnik and Hoheisel), and making advances that seemed inaccessible to classical methods. Now the principal investigator wishes to understand the existence of, and evaluate, mean values, find how to integrate triple products (to show there are primes in short intervals), find higher order cancelation, study higher weight L-functions, develop links to additive combinatorics and to the sieve, and exploit the dispersion method.
Programme
Canada Research Chairs
Bénéficiaire
Emplacement
Quebec, Canada
Type de bénéficiaire
Academia
Type
Grant
Source
NSERC's Awards Data
Tel que publié
Application id
CRC-2015-00021
Name nom
Granville, Andrew
Department département
mathematics - Université de Montréal
Organization id
63
Institution établissement
Université de Montréal
Province en
Québec
Province fr
Québec
Country en
CANADA
Country fr
CANADA
Fiscal year exercice financier
2023
Competition year année de concours
2015
Award amount
200000
Program id
CRC
Program name en
Canada Research Chairs
Program name fr
Chaires de recherche du Canada
Group en
DISCOVERY RESEARCH
Group fr
RECHERCHE AXÉE SUR LA DÉCOUVERTE
Committee code
9998
Committee name en
Canada Research Chair Selection Committee
Committee name fr
Comité de sélection des Chaires de recherche du Canada
Area of application code
9999
Area of application group en
Not available
Area of application group fr
Non disponible
Area of application en
Not available
Area of application fr
Non disponible
Research subject code
10000
Research subject group en
The field of research available
Research subject group fr
The field of research available
Research subject en
Le domaine de recherche disponible
Research subject fr
Le domaine de recherche disponible
Field of research list codes
RDF10101
Field of research list names en
Pure mathematics
Field of research list names fr
Mathématiques pures
Application title
number theory
Keyword
Multiplicative functions
analytic number theory
L-functions
Riemann zeta-function
additive combinatorics
dispersion method
Perron¿s formula
Application summary
The principal investigator is developing an alternative approach to analytic number theory, the first coherent program since Riemann's 1859 memoir. He can now reprove all classical results, quantitatively and qualitatively, providing simpler proofs of notoriously difficult results (E.g Theorems of Linnik and Hoheisel), and making advances that seemed inaccessible to classical methods. Now the principal investigator wishes to understand the existence of, and evaluate, mean values, find how to integrate triple products (to show there are primes in short intervals), find higher order cancelation, study higher weight L-functions, develop links to additive combinatorics and to the sieve, and exploit the dispersion method.
