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Interplay of multiplicative number theory and additive combinatorics

Description du projet

Examiner les liens entre la théorie multiplicative des nombres et la combinatoire additive

La théorie multiplicative des nombres est une branche de la théorie du même nom qui porte sur les nombres premiers et les fonctions multiplicatives. L’une des grandes questions ouvertes dans le domaine est la conjecture de Chowla, qui avance que les décompositions en facteurs premiers de nombres consécutifs devraient se comporter indépendamment les unes des autres. Financé par le programme Actions Marie Skłodowska-Curie, le projet MultNT entend étudier plus avant la conjecture de Chowla, ainsi que d’autres questions clés dans la théorie multiplicative des nombres. Ce projet examinera également les liens entre la conjecture de Chowla et la combinatoire additive et l’analyse de Fourier d’ordre supérieur. En outre, MultNT s’intéressera à la conjecture de Hardy-Littlewood en moyenne et au principe de Hasse pour presque toutes les surfaces d’un certain type.

Objectif

This project concerns multiplicative number theory and its interplay with the emerging topic of additive combinatorics. Multiplicative number theory is an area of number theory concerned with the study of prime numbers and multiplicative functions. One of the most important unsolved questions in this area and in all of number theory is the twin prime conjecture, asserting that there are infinitely many pairs of prime numbers differing by two.

In 1965, Chowla formulated an influential conjecture that can be viewed as an approximation to the twin prime conjecture. Chowla’s conjecture predicts that the prime factorisations of consecutive integers behave independently of each other. This conjecture captures the key difficulty in the twin prime conjecture, but yet there has been a lot of recent progress on Chowla’s conjecture by the applicant and others.

The aim of this project is to make substantial progress on Chowla’s conjecture, as well as on other key questions in multiplicative number theory, using a mixture of methods from analytic number theory and additive combinatorics, as well as higher order Fourier analysis, a theory recently developed by Green and Tao. Connections between Chowla’s conjecture and questions in additive combinatorics and higher order Fourier analysis have recently been discovered in works of the applicant and others, and the proposed research aims at exploiting these connections to make substantial progress on Chowla’s conjecture. The project also involves several other problems of interest in number theory, such as the Hardy—Littlewood conjecture on average and the Hasse principle for almost all surfaces of a certain type.

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Coordinateur

TURUN YLIOPISTO
Contribution nette de l'UE
€ 215 534,40
Adresse
Yliopistonmaki
20014 Turku
Finlande

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Région
Manner-Suomi Etelä-Suomi Varsinais-Suomi
Type d’activité
Higher or Secondary Education Establishments
Liens
Contribution de l’UE
Aucune donnée