7 papers
The divisor function along arithmetic progressions and binary cubic polynomials
Lasse Grimmelt, Jori Merikoski
We prove a new equidistribution estimate for the divisor function in arithmetic progression to moduli that have two small factors. We give two applications. First, we show an asymp…
On the greatest prime factor and uniform equidistribution of quadratic polynomials
Lasse Grimmelt, Jori Merikoski
We show that the greatest prime factor of is at least infinitely often. This gives an unconditional proof for the range previously known under the Selberg eigen…
Weighted averages of automorphic kernel, Part I: non-oscillatory functions
Lasse Grimmelt, Jori Merikoski
We prove a theorem that evaluates weighted averages of sums parametrised by congruence subgroups of . In the proof, spectral methods are applied di…
On primes represented by
Jori Merikoski
Let be coprime integers. Assuming a conjecture on Hecke eigenvalues along binary cubic forms, we prove an asymptotic formula for the number of primes of the form $ax^2+by^3…
On Gaussian primes in sparse sets
Jori Merikoski
We show that there exists some such that, for any set of integers with for all , there are infinitely many primes of the form $a^2+b^2…
Twisted correlations of the divisor function via discrete averages of Poincaré series
Lasse Grimmelt, Jori Merikoski
We prove a theorem that allows one to count solutions to determinant equations twisted by a periodic weight with high uniformity in the modulus. It is obtained by using spectral me…