38 citations · 177 across the 23 of their papers we have counts for
26 papers
Quantitative Gowers uniformity of the primes in intervals of length
Joni Teräväinen
We prove the first quantitative bounds for the Gowers norms of the von Mangoldt function minus a Siegel corrected model function in short intervals. The result applies to intervals…
Sum-product patterns in the shifted primes
Florian K. Richter, Joni Teräväinen
We show that the set of shifted primes contains infinitely many sum-product patterns of the form with arbitrarily large distinct integers. More…
On the generation of multiplicative groups by small primes
Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen
Motivated by a question of Regev arising from his improved quantum factoring algorithm, we study how many small primes are needed to generate the group $({\mathbb Z}/q{\mathbb Z})^…
On the local Fourier uniformity problem for small sets
Adam Kanigowski, Mariusz Lemańczyk, Florian Karl Richter +1
We consider vanishing properties of exponential sums of the Liouville function of the form $$ \lim_{H\to\infty}\limsup_{X\to\infty}\frac{1}{\log X}\sum_{m\leq X}\frac{1}{m}\sup…
On a Bohr set analogue of Chowla's conjecture
Joni Teräväinen, Aled Walker
Let denote the Liouville function. We show that the logarithmic mean of is whenever are positive reals with $α_1/α_…
Gaussian almost primes in almost all narrow sectors
Olli Järviniemi, Joni Teräväinen
We show that almost all sectors of the disc of area contain products of exactly two Gaussian primes, and that almost all secto…
Products of primes in arithmetic progressions
Kaisa Matomäki, Joni Teräväinen
A conjecture of Erdős states that, for any large prime , every reduced residue class can be represented as a product of two primes . We establi…
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
Tim Browning, Efthymios Sofos, Joni Teräväinen
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish…
Higher uniformity of arithmetic functions in short intervals I. All intervals
Kaisa Matomäki, Xuancheng Shao, Terence Tao +1
We study higher uniformity properties of the Möbius function , the von Mangoldt function , and the divisor functions on short intervals with $X^{θ+\varepsilon…
Beyond the Erdős discrepancy problem in function fields
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We characterize the limiting behavior of partial sums of multiplicative functions . In contrast to the number field setting, the characterization depends…
On the Hardy-Littlewood-Chowla conjecture on average
Jared Duker Lichtman, Joni Teräväinen
There has been recent interest in a hybrid form of the celebrated conjectures of Hardy-Littlewood and of Chowla. We prove that for any and distinct integers $h_2,\ldot…
The Hardy--Littlewood--Chowla conjecture in the presence of a Siegel zero
Terence Tao, Joni Teräväinen
Assuming that Siegel zeros exist, we prove a hybrid version of the Chowla and Hardy--Littlewood prime tuples conjectures. Thus, for an infinite sequence of natural numbers , and…
Quantitative bounds for Gowers uniformity of the Möbius and von Mangoldt functions
Terence Tao, Joni Teräväinen
We establish quantitative bounds on the Gowers norms of the Möbius function and the von Mangoldt function for all , with error terms of shape $O((\log\log N)^{-…
A transference principle for systems of linear equations, and applications to almost twin primes
Pierre-Yves Bienvenu, Xuancheng Shao, Joni Teräväinen
The transference principle of Green and Tao enabled various authors to transfer Szemerédi's theorem on long arithmetic progressions in dense sets to various sparse sets of integers…
On the Liouville function at polynomial arguments
Joni Teräväinen
Let denote the Liouville function. A problem posed by Chowla and by Cassaigne-Ferenczi-Mauduit-Rivat-Sárközy asks to show that if , then the sequence $λ(…
Composite values of shifted exponentials
Olli Järviniemi, Joni Teräväinen
A well-known open problem asks to show that is composite for almost all values of . This was proposed by Gil Kalai as a possible Polymath project, and was posed original…
Correlations of multiplicative functions in function fields
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We develop an approach to study character sums, weighted by a multiplicative function , of the form \begin{equation} \sum_{G\in \mathcal{M}_N}f(G)χ(G)ξ(G)…
The Bombieri-Vinogradov theorem for nilsequences
Xuancheng Shao, Joni Teräväinen
We establish results of Bombieri-Vinogradov type for the von Mangoldt function twisted by a nilsequence. In particular, we obtain Bombieri-Vinogradov type results for the vo…
On the Möbius function in all short intervals
Kaisa Matomäki, Joni Teräväinen
We show that, for the Möbius function , we have for any . This improves on a result of Ramachandra from 1976, which is valid f…
Multiplicative functions that are close to their mean
Oleksiy Klurman, Alexander P. Mangerel, Cosmin Pohoata +1
We introduce a simple sieve-theoretic approach to studying partial sums of multiplicative functions which are close to their mean value. This enables us to obtain various new resul…
Multiplicative functions in short arithmetic progressions
Oleksiy Klurman, Alexander P. Mangerel, Joni Teräväinen
We study for bounded multiplicative functions sums of the form \begin{align*} \sum_{\substack{n\leq x \atop n\equiv a\pmod q}}f(n), \end{align*} establishing that their varianc…
Odd order cases of the logarithmically averaged Chowla conjecture
Terence Tao, Joni Teräväinen
A famous conjecture of Chowla states that the Liouville function has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmi…
On binary correlations of multiplicative functions
Joni Teräväinen
We study logarithmically averaged binary correlations of bounded multiplicative functions and . A breakthrough on these correlations was made by Tao, who showed that the…
The structure of logarithmically averaged correlations of multiplicative functions, with applications to the Chowla and Elliott conjectures
Terence Tao, Joni Teräväinen
Let be -bounded multiplicative functions, and let be shifts. We consider correlation sequences $f: {\bf N} \to {…