11 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…
A Cubic analogue of the Friedlander-Iwaniec spin over primes
Jori Merikoski
In 1998 Friedlander and Iwaniec proved that there are infinitely many primes of the form . To show this they defined the spin of Gaussian integers by the Jacobi symbol, an…
On the largest prime factor of
Jori Merikoski
We show that the largest prime factor of is infinitely often greater than . This improves the result of de la Bretèche and Drappeau (2019) who obtained this with…