1 citations · 1 across the 9 of their papers we have counts for
10 papers
Quantitative bounds for sets lacking polynomial progressions with shifted prime difference
Ben Krause, Hamed Mousavi, Terence Tao +1
We prove quantitative polynomial Szemerédi-type theorems involving polynomial progressions with shift parameter restricted to the set of shifted primes . The types of…
Gilbreath's conjecture: a Cramér random model and a deterministic analysis
Zachary Chase, Zach Hunter, Terence Tao
Gilbreath's conjecture asserts that if one starts with the sequence of primes and takes successive absolute differences to create a triangular array, then the left diagonal of this…
Products of consecutive integers with unusual anatomy
Terence Tao
Call an interval of consecutive natural numbers \emph{bad} if the product is divisible by the square of its largest prime factor; \emph{very…
Local Bernstein theory, and lower bounds for Lebesgue constants
Terence Tao
Classical (or ``global'') Bernstein theory establishes sharp control on entire functions of exponential type that are bounded and real-valued on the real axis. We localize some of…
Quantitative correlations and some problems on prime factors of consecutive integers
Terence Tao, Joni Teräväinen
We consider several old problems involving the number of prime divisors function , as well as the related functions and . Firstly, we show that there are infinit…
Rough numbers between consecutive primes
Ayla Gafni, Terence Tao
Using a sieve-theoretic argument, we show that almost all gaps between consecutive primes contain a natural number whose least prime factor $p(m…
On the number of exceptional intervals to the prime number theorem in short intervals
Ayla Gafni, Terence Tao
For a fixed exponent , it is expected that we have the prime number theorem in short intervals as . From the rece…
Decomposing a factorial into large factors
Boris Alexeev, Evan Conway, Matthieu Rosenfeld +4
Let denote the largest number such that can be expressed as the product of integers greater than or equal to . The bound was apparently es…
Higher uniformity of arithmetic functions in short intervals II. Almost all intervals
Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao +2
We study higher uniformity properties of the von Mangoldt function , the Möbius function , and the divisor functions on short intervals for almost all $x \in…
Pointwise convergence of bilinear polynomial averages over the primes
Ben Krause, Hamed Mousavi, Terence Tao +1
We show that on a -finite measure preserving system , the non-conventional ergodic averages converge pointw…