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On the representation of primes by binary quadratic forms, and elliptic curves

Abstract:

It is shown that, under some mild technical conditions, representations of prime numbers by binary quadratic forms can be computed in polynomial complexity by exploiting Schoof's algorithm, which counts the number of $\mathbb F_q$-points of an elliptic curve over a finite field $\mathbb F_q$. Further, a method is described which computes representations of primes from reduced quadratic forms by means of the integral roots of polynomials over $\mathbb Z$. Lastly, some progress is made on the s...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.17654/NT040020165

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
ORCID:
0000-0002-7985-3131
Publisher:
Pushpa Publishing House Publisher's website
Journal:
JP Journal of Algebra, Number Theory and Applications Journal website
Volume:
40
Issue:
2
Pages:
165-179
Publication date:
2018-04-01
Acceptance date:
2017-12-05
DOI:
Pubs id:
pubs:861754
URN:
uri:3a8e0cf3-0a46-4bae-8351-4f3dc33f3f99
UUID:
uuid:3a8e0cf3-0a46-4bae-8351-4f3dc33f3f99
Local pid:
pubs:861754

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