JP Journal of Algebra, Number Theory and Applications
Volume 40, Issue 2, Pages 165 - 179
(April 2018) http://dx.doi.org/10.17654/NT040020165 |
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ON THE REPRESENTATION OF PRIMES BY BINARY QUADRATIC FORMS
Michele Elia and Federico Pintore
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Abstract: The old problem of computing the representation of a prime p by a given quadratic form of discriminant D is considered. This representation problem is shown to be solvable, under mild technical conditions, in polynomial complexity with respect to p. Further, a method is proposed which obtains the explicit representation of p by the integer roots of univariate polynomials. |
Keywords and phrases: quadratic field, binary quadratic form, representation of primes, Hilbert class polynomial, elliptic curve. |
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