6 citations · 7 across the 12 of their papers we have counts for
12 papers
The exceptional set of the Goldbach problem
Gautami Bhowmik, Lasse Grimmelt
We study the estimates for the number of exceptions to the representation of integers as the sum of at most two prime numbers. Most of this article is a survey that gives an overvi…
Random linear configurations in dense sets and primes
Lasse Grimmelt, Joni Teräväinen
We prove that every polylogarithmically dense subset of contains a nontrivial configuration for almost all choices of the coefficient vector $(b_1,\ldo…
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…
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…
On an Erdős--Kac-type conjecture of Elliott
Ofir Gorodetsky, Lasse Grimmelt
Elliott and Halberstam proved that is asymptotic to . In analogy to the Erdős--Kac Theorem, Elliott conjectured that if one restricts the summation to…
The Exceptional Set in Goldbach's Problem with Almost Twin Primes
Lasse Grimmelt, Joni Teräväinen
We consider the exceptional set in the binary Goldbach problem for sums of two almost twin primes. Our main result is a power-saving bound for the exceptional set in the problem of…
Representation of Squares by Nonsingular Cubic Forms
Lasse Grimmelt, Will Sawin
We prove an asymptotic formula for the number of representations of squares by nonsingular cubic forms in six or more variables. The main ingredients of the proof are Heath-Brown's…
Goldbach Numbers in Short Intervals -- A Nonnegative Model Approach
Lasse Grimmelt
We decrease the length of the shortest interval for which almost all even integers in it are the sum of two primes. This is achieved by applying a version of the Circle Method that…
Vinogradov's Theorem with Fouvry-Iwaniec Primes
Lasse Grimmelt
We show that every sufficiently large can be written as the sum of three primes, each of which is a sum of a square and a prime square. The main tools are a transfer…