Lasse Grimmelt

Primes and Quadratic Polynomials

Generalising a famous conjecture of Landau, we expect that for any fixed positive integer $h$ there should be infinitely many prime values of the quadratic polynomial $n^2+h$. Two cornerstones of modern analytic number theory naturally appear when studying this problem: Combinatorial decompositions and the spectral theory of automorphic forms. Based on a new way of applying spectral methods, recently J. Merikoski and I improved the size of the largest prime divisor of these quadratic polynomials. Furthermore, in upcoming work with J. Merikoski and M. Pandey, we consider the problem on average of $h$.