Analytic Number Theory

Analytic Number Theory has seen numerous breakthroughs on very fundamental questions during recent years. These include spectacular results on progressions in the primes and prime gaps both large and small. Apart from prime number theory, multiplicative number theory has also seen major progress, for example several breakthroughs on multiplicative functions in short intervals, e.g. relating to the Erdős Discrepancy problem. The theory of automorphic forms and their L-functions is also central in modern number theory, linking diverse areas of mathematics like analysis, representation theory, algebraic geometry to name a few. Recently there have been several strong results about moments of central L-values supporting random matrix theory predictions, results on equidistribution and other types of distributions, density theorems verifying cases of Sarnak’s conjecture, and many other remarkable advances.