This project on pure mathematics, to be conducted at the University of Turku, concerns analytic number theory, additive combinatorics, and in particular their applications to the theory of multiplicative functions and the primes. A central question in the research is Chowla's conjecture from the 1960s on the correlations of the Möbius function, as well as Elliott's conjecture that generalizes it. This conjecture is an approximation to the twin prime conjecture from the 1800s, which is one of the greatest unsolved problems in number theory. The results of the research are expected to have applications to e.g. variants of the Erdös discrepancy problem and to generalizations of the Green-Tao theorem. The methods used in the research include in addition to techniques from number theory and combinatorics also at least ergodic theory and higher order Fourier analysis.

2021

2022