The differences between consecutive primes, V

The differences between consecutive primes, V

We show that ∑ pn≤x pn+1−pn≥ √ pn (pn+1−pn)≪εx3/5+ε or any fixed ε>0⁠. This improves a result of Matomäki, in which the exponent was 2/3⁠.

Bibliografiske detaljer
Hovedforfatter:	Heath-Brown, D
Format:	Journal article
Sprog:	English
Udgivet:	Oxford University Press 2019

Lignende værker

A note on the differences between consecutive primes
af: Heath-Brown, D, et al.
Udgivet: (1984)

The differences between consecutive smooth numbers
af: Heath-Brown, D
Udgivet: (2018)

Large gaps between consecutive prime numbers
af: Ford, K, et al.
Udgivet: (2016)

The square sieve and consecutive square-free numbers
af: Heath-Brown, D
Udgivet: (1984)

Almost-prime k-tuples
af: Heath-Brown, D
Udgivet: (1997)

Lagrange's four squares theorem with one prime and three almost-prime variables
af: Heath-Brown, D, et al.
Udgivet: (2003)

Lagrange's four squares theorem with one prime and three almost--prime variables
af: Heath-Brown, D, et al.
Udgivet: (2003)

The Pjateckiǐ-Šapiro prime number theorem
af: Heath-Brown, D
Udgivet: (1983)

The largest prime factor of the integers in an interval
af: Heath-Brown, D
Udgivet: (1996)

Carmichael numbers with three prime factors
af: Heath-Brown, D
Udgivet: (2007)

Primes represented by cubic forms
af: Heath-Brown, D, et al.
Udgivet: (2002)

The largest prime factor of X-3+2
af: Heath-Brown, D
Udgivet: (2001)

Siegel zeros and the least prime in an arithmetic progression
af: Heath-Brown, D
Udgivet: (1990)

Prime number theory and the Riemann zeta-function
af: Heath-Brown, D
Udgivet: (2005)

Prime number theory and the Riemann Zeta-function
af: Heath-Brown, D
Udgivet: (2005)

The largest prime factor of $X^3+2$
af: Heath-Brown, D
Udgivet: (2001)

Primes represented by x(3)+2y(3)
af: Heath-Brown, D
Udgivet: (2001)

Primes represented by $x^3+2y^3$
af: Heath-Brown, D
Udgivet: (2001)

Primes represented by binary cubic forms
af: Heath-Brown, D, et al.
Udgivet: (2002)

Almost prime triples and Chen's theorem
af: Heath-Brown, D, et al.
Udgivet: (2016)

The largest prime factor of the integers in an interval, II
af: Heath-Brown, D, et al.
Udgivet: (1998)

On the representation of primes by cubic polynomials in two variables
af: Heath-Brown, D, et al.
Udgivet: (2004)

Prime values of a^2+p^4
af: Heath-Brown, D, et al.
Udgivet: (2016)

On the representation of primes by cubic polynomials in two variables
af: Heath-Brown, D, et al.
Udgivet: (2004)

Investigating the difference between the acute effects of consecutive and non-consecutive days of resistance exercise on the immune system
af: Teo, Hilary Wei Jian
Udgivet: (2016)

Integers represented as a sum of primes and powers of two
af: Heath-Brown, D, et al.
Udgivet: (2002)

Primes represented by x3 + 2y3
af: Heath-Brown, DR
Udgivet: (2001)

Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression
af: Heath-Brown, D
Udgivet: (1992)

On the difference of values of the kernel function at consecutive integers
af: Jean-Marie De Koninck, et al.
Udgivet: (2003-01-01)

Parallel translation process in consecutive interpreting: Differences between beginning and advanced interpreting students
af: Deyan Zou, et al.
Udgivet: (2024-08-01)

Difference sets and the primes
af: Ruzsa, I, et al.
Udgivet: (2008)

Genetic components affecting the interval between consecutive inseminations
af: Kräusslich H, et al.
Udgivet: (1978-10-01)

Gaps between primes
af: Maynard, J
Udgivet: (2019)

A Collaborative Approach to Retention Between Academic Affairs and Student Affairs: The Two Consecutive Absence Policy
af: Stuart Brown, et al.
Udgivet: (2018-03-01)

IFT trains in different stages of assembly queue at the ciliary base for consecutive release into the cilium
af: Jenna L Wingfield, et al.
Udgivet: (2017-05-01)

Focal atrial tachycardia-the localization differences between men and women: A study of 487 consecutive patients
af: Yusuf Turkmen, et al.
Udgivet: (2020-11-01)

Some "prime" comparisons /
af: 365541 Brown, Stephen I.
Udgivet: (1978)

Learning needs analysis at different stages of an undergraduate course in consecutive interpreting
af: Zohreh Gharaei, et al.
Udgivet: (2024-02-01)

Different levels of undermining in face lift - Experience of 141 consecutive cases
af: Panettiere Pietro, et al.
Udgivet: (2004-01-01)

The role of nitric oxide in small intestine differs between a single and a consecutive administration of methotrexate to rats
af: Saki Shiga, et al.
Udgivet: (2020-05-01)