Genus theory and the factorization of class equations over\n mathbbF_p

2014/09/02 by Patrick Morton, Morton, Patrick
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1409.0691

openalex publication_date 2014/09/02 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

A new proof, depending only on genus theory, is given of a theorem of\nStankewicz, which characterizes the primes p for which the class equation\nH_D(X) of the maximal order of the imaginary quadratic field\nK=\ℚ(\√(D)) has a linear factor (mod p). This yields a prime\ndecomposition law for the primes p with p nmid D in the real subfield of\nthe Hilbert class field of K.\n

Related

• Genus theory, governing field, ramification and Frobenius
• The genus fields of Artin-Schreier extensions
• Factorization of Hilbert class polynomials over prime fields
• Successive maxima of the non-genus part of class numbers
• On the strongly ambiguous classes of some biquadratic number fields