# Journal article

## Triangles with prime hypotenuse

Abstract:

The sequence 3,5,9,11,15,19,21,25,29,35,… consists of odd legs in right triangles with integer side lengths and prime hypotenuse. We show that the upper density of this sequence is zero, with logarithmic decay. The same estimate holds for the sequence of even legs in such triangles. We expect our upper bound, which involves the Erdős–Ford–Tenenbaum constant, to be sharp up to a double-logarithmic factor. We also provide a nontrivial lower bound. Our techniques involve sieve methods, the distr...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Version of record, pdf, 634.8KB)
Publisher copy:
10.1007/s40993-017-0086-6

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Department:
Unknown
Role:
Author
More by this author
Role:
Author
ORCID:
0000-0002-0960-1692
Publisher:
Springer Open Publisher's website
Journal:
Research in Number Theory Journal website
Volume:
3
Issue:
1
Article number:
21
Publication date:
2017-10-09
Acceptance date:
2017-06-27
DOI:
ISSN:
2363-9555
Keywords:
Pubs id:
pubs:926124
UUID:
uuid:24e35e17-405e-40cd-bfec-85052f1b1c88
Local pid:
pubs:926124
Source identifiers:
926124
Deposit date:
2018-10-10