From the 2 of 6 linked papers with an AI index.
6 papers
Random linear configurations in dense sets and primes
Lasse Grimmelt, Joni Teräväinen
The paper shows that any subset of the integers up to N that is dense at a polylogarithmic level contains nontrivial linear configurations of the form x+b₁m,…,x+b_km for most coeff…
The exceptional set of the Goldbach problem
Lasse Grimmelt, Gautami Bhowmik
The paper surveys known results on the size of the exceptional set for representing integers as sums of at most two primes, reviews the Hardy‑Littlewood circle method and later pow…
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…
The Exceptional Set in Goldbach's Problem with two Chen Primes
Lasse Grimmelt, Joni Teräväinen
We show that all natural numbers are the sum of two Chen primes (primes such that has at most two prime factors), apart from a power-saving set of exce…
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…