276 citations · 4.5k across the 293 of their papers we have counts for
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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…
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)^{-…
Singmaster's conjecture in the interior of Pascal's triangle
Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao +2
Singmaster's conjecture asserts that every natural number greater than one occurs at most a bounded number of times in Pascal's triangle; that is, for any natural number …
Large prime gaps and probabilistic models
William Banks, Kevin Ford, Terence Tao
We introduce a new probabilistic model of the primes consisting of integers that survive the sieving process when a random residue class is selected for every prime modulus below a…
Value patterns of multiplicative functions and related sequences
Terence Tao, Joni Teräväinen
We study the existence of various sign and value patterns in sequences defined by multiplicative functions or related objects. For any set whose indicator function is 'approxim…