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# The decomposition of primes in torsion point fields

Author: Clemens Adelmann Berlin ; New York : Springer, ©2001. Lecture notes in mathematics (Springer-Verlag), 1761. eBook : Document : EnglishView all editions and formats We investigate the decomposition of prime ideals in non-abelian extensions of number fields. These fields are generated by the coordinates of torsion points of elliptic curves without complex multiplications. We explain the necessary prerequisites from the theory of elliptic curves, modular forms, algebraic number theory, and invariant theory. Due to the complexity of the problem, complete results are restricted to torsion points of low order. These results are complemented by computational data which also cover some unsolved cases.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version:Adelmann, Clemens, 1965-Decomposition of primes in torsion point fields.New York : Springer, ©2001(DLC) 2001031199(OCoLC)46809048 Document, Internet resource Internet Resource, Computer File Clemens Adelmann Find more information about: Clemens Adelmann 9783540449492 3540449493 50398222 1 online resource (vi, 142 pages) : illustrations. Introduction -- Decomposition laws -- Elliptic curves -- Elliptic modular curves -- Torsion point fields -- Invariants and resolvent polynomials -- Appendix: Invariants of elliptic modular curves; L-series coefficients a p; Fully decomposed prime numbers; Resolvent polynomials; Free resolution of the invariant algebra. Lecture notes in mathematics (Springer-Verlag), 1761. Clemens Adelmann.

### Abstract:

k k Given an extension K/k of algebraic number ?elds and a prime ideal p of O , the decomposition law of K/k describes the product decomposition of k the ideal generated by p in O and names its  Read more...

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