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The Goldbach problem for primes that are sums of two squares plus one

Abstract:

We study the Goldbach problem for primes represented by the polynomial $x^2+y^2+1$. The set of such primes is sparse in the set of all primes, but the infinitude of such primes was established by Linnik. We prove that almost all even integers $n$ satisfying certain necessary local conditions are representable as the sum of two primes of the form $x^2+y^2+1$. This improves a result of Matomäki, which tells that almost all even $n$ satisfying a local condition are the sum of one prime of the fo...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/S0025579317000341

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Institution:
University of Oxford
Division:
Mathematical, Physical and Life Sciences Division
Department:
Mathematical Institute
Role:
Author
University of Turku Graduate School More from this funder
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Grant:
project number 293876
Publisher:
University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics Publisher's website
Journal:
Mathematika Journal website
Volume:
64
Issue:
1
Pages:
20-70
Publication date:
2018-01-25
Acceptance date:
2018-01-25
DOI:
EISSN:
2041-7942
ISSN:
0025-5793
Pubs id:
pubs:935444
URN:
uri:640f289e-28e7-4a71-bc2d-0624ac740e09
UUID:
uuid:640f289e-28e7-4a71-bc2d-0624ac740e09
Local pid:
pubs:935444

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