Jori Merikoski

activity

20162025

most citedLimit points of normalized prime gaps

4 citations · 4 across the 15 of their papers we have counts for

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17 papers · 1 filter

math.NT2025

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…

math.NT2025

On the greatest prime factor and uniform equidistribution of quadratic polynomials

Lasse Grimmelt, Jori Merikoski

We show that the greatest prime factor of $n^{2} + h$ is at least $n^{1.312}$ infinitely often. This gives an unconditional proof for the range previously known under the Selberg eigen…

math.NT2025

Weighted averages of $SL_{2} (R)$ 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 $SL_{2} (Z)$ . In the proof, spectral methods are applied di…

math.NT2025

On primes represented by $a X^{2} + b Y^{3}$

Jori Merikoski

Let $a, b > 0$ 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…

math.NT2024

Twisted correlations of the divisor function via discrete averages of $SL_{2} (R)$ 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…

math.NT2024

Primes in arithmetic progressions and short intervals without $L$ -functions

Kaisa Matomäki, Jori Merikoski, Joni Teräväinen

We develop a sieve that can detect primes in multiplicatively structured sets under certain conditions. We apply it to obtain a new $L$ -function free proof of Linnik's problem of b…

math.NT2023

On Gaussian primes in sparse sets

Jori Merikoski

We show that there exists some $δ > 0$ such that, for any set of integers $B$ with $B \cap [1, Y] ≫ Y^{1 - δ}$ for all $Y ≫ 1$ , there are infinitely many primes of the form $a^{2} + b^{2}$ …

math.NT2021

The polynomials $X^{2} + (Y^{2} + 1)^{2}$ and $X^{2} + (Y^{3} + Z^{3})^{2}$ also capture their primes

Jori Merikoski

We show that there are infinitely many primes of the form $X^{2} + (Y^{2} + 1)^{2}$ and $X^{2} + (Y^{3} + Z^{3})^{2}$ . This extends the work of Friedlander and Iwaniec showing that there are infinitely…

math.NT2021

Exceptional characters and prime numbers in sparse sets

Jori Merikoski

We develop a lower bound sieve for primes under the (unlikely) assumption of infinitely many exceptional characters. Compared with the illusory sieve due to Friedlander and Iwaniec…

math.NT2020

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 $a^{2} + b^{4}$ . To show this they defined the spin of Gaussian integers by the Jacobi symbol, an…

math.NT2020

On totally split primes in high-degree torsion fields of elliptic curves

Jori Merikoski

Analogously to primes in arithmetic progressions to large moduli, we can study primes that are totally split in extensions of $Q$ of high degree. Motivated by a question o…

math.NT2019

On the largest prime factor of $n^{2} + 1$

Jori Merikoski

We show that the largest prime factor of $n^{2} + 1$ is infinitely often greater than $n^{1.279}$ . This improves the result of de la Bretèche and Drappeau (2019) who obtained this with…

math.NT2019

On the largest square divisor of shifted primes

Jori Merikoski

We show that there are infinitely many primes $p$ such that $p - 1$ is divisible by a square $d^{2} \geq p^{θ}$ for $θ = 1/2 + 1/2000.$ This improves the work of Matomäki (2009) who obtained…

math.NT2018★ 4 cited

Limit points of normalized prime gaps

Jori Merikoski

We show that at least 1/3 of positive real numbers are in the set of limit points of normalized prime gaps. More precisely, if $p_{n}$ denotes the $n$ th prime and $L$ is the…

math.NT2018

Large prime factors on short intervals

Jori Merikoski

We show that for all large enough $x$ the interval $[x, x + x^{1/2} lo g^{1.39} x]$ contains numbers with a prime factor $p > x^{18/19} .$ Our work builds on the previous works of Heath-…

math.NT2016

Averaged Form of the Hardy-Littlewood Conjecture

Jori Merikoski

We study the prime pair counting functions $π_{2 k} (x),$ and their averages over $2 k .$ We show that good results can be achieved with relatively little effort by considering average…

math.NT2016

Applying Discrete Fourier Transform to the Hardy-Littlewood Conjecture

Jori Merikoski

We study the asymptotic behaviour of the prime pair counting function $π_{2 k} (n)$ by the means of the discrete Fourier transform on $Z / n Z$ . The method we develop…

The divisor function along arithmetic progressions and binary cubic polynomials

On the greatest prime factor and uniform equidistribution of quadratic polynomials

Weighted averages of SL2​(R) automorphic kernel, Part I: non-oscillatory functions

On primes represented by aX2+bY3

Twisted correlations of the divisor function via discrete averages of SL2​(R) Poincaré series

Primes in arithmetic progressions and short intervals without L-functions

On Gaussian primes in sparse sets

The polynomials X2+(Y2+1)2 and X2+(Y3+Z3)2 also capture their primes

Exceptional characters and prime numbers in sparse sets

A Cubic analogue of the Friedlander-Iwaniec spin over primes

On totally split primes in high-degree torsion fields of elliptic curves

On the largest prime factor of n2+1

On the largest square divisor of shifted primes

Limit points of normalized prime gaps

Large prime factors on short intervals

Averaged Form of the Hardy-Littlewood Conjecture

Applying Discrete Fourier Transform to the Hardy-Littlewood Conjecture

Weighted averages of $SL_{2} (R)$ automorphic kernel, Part I: non-oscillatory functions

On primes represented by $a X^{2} + b Y^{3}$

Twisted correlations of the divisor function via discrete averages of $SL_{2} (R)$ Poincaré series

Primes in arithmetic progressions and short intervals without $L$ -functions

The polynomials $X^{2} + (Y^{2} + 1)^{2}$ and $X^{2} + (Y^{3} + Z^{3})^{2}$ also capture their primes

On the largest prime factor of $n^{2} + 1$