English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the exceptional set in the binary Goldbach problem for sums oftwo almost twin primes. Our main result is a power-saving bound for theexceptional set in the problem of representing $m=p_1+p_2$ where $p_1+2$ has atmost $2$ prime divisors and $p_2+2$ has at most $3$ prime divisors. There arethree main ingredients in the proof: a new transference principle like approachfor sieves, a combination of the level of distribution estimates ofBombieri--Friedlander--Iwaniec and Maynard with ideas of Drappeau to producepower savings, and a generalisation of the circle method arguments ofMontgomery and Vaughan that incorporates sieve weights.

The Exceptional Set in Goldbach's Problem with Almost Twin Primes