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- Discriminant_of_an_algebraic_number_field abstract "In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking, measures the size of the (ring of integers of the) algebraic number field. More specifically, it is proportional to the volume of the fundamental domain of the ring of integers, and it regulates which primes are ramified.The discriminant is one of the most basic invariants of a number field, and occurs in several important analytic formulas such as the functional equation of the Dedekind zeta function of K, and the analytic class number formula for K. An old theorem of Hermite states that there are only finitely many number fields of bounded discriminant, however determining this quantity is still an open problem, and the subject of current research.The discriminant of K can be referred to as the absolute discriminant of K to distinguish it from the relative discriminant of an extension K/L of number fields. The latter is an ideal in the ring of integers of L, and like the absolute discriminant it indicates which primes are ramified in K/L. It is a generalization of the absolute discriminant allowing for L to be bigger than Q; in fact, when L = Q, the relative discriminant of K/Q is the principal ideal of Z generated by the absolute discriminant of K.".
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Adjunction_(field_theory).
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Alexander_von_Brill.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Algebraic_number_field.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Analytic_number_theory.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Artin_conductor.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Brauer–Siegel_theorem.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Cambridge_University_Press.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Category:Algebraic_number_theory.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Character_group.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Charles_Hermite.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Class_number_formula.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Complex_number.
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Degree_of_a_field_extension.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Determinant.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Different_ideal.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Discriminant.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Eulers_totient_function.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Field_extension.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Field_norm.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Field_trace.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Functional_equation_(L-function).
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Fundamental_discriminant.
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Galois_group.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Generalized_Riemann_hypothesis.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Golod–Shafarevich_theorem.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Hermite–Minkowski_theorem.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Hilbert_class_field.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ideal_(ring_theory).
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ideal_class_group.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ideal_norm.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Injective_function.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Invariant_(mathematics).
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Isomorphism.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Leopold_Kronecker.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ludwig_Stickelberger.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Mathematics.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Matrix_(mathematics).
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Measure_(mathematics).
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Minimal_polynomial_(field_theory).
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Monogenic_field.
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ramification_(mathematics).
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Richard_Dedekind.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ring_homomorphism.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Ring_of_integers.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Root_of_unity.
- Discriminant_of_an_algebraic_number_field wikiPageWikiLink Sign_(mathematics).
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- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "''discriminant''".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "Discriminant of an algebraic number field".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "Discriminant of an algebraic number field#Basic results".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "Discriminant of an algebraic number field#RelativeDiscriminant".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "Discriminant of an algebraic number field#Root discriminant".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "algebraic number fields".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "discriminant of an algebraic number field".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "discriminant".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "field discriminant".
- Discriminant_of_an_algebraic_number_field wikiPageWikiLinkText "relative discriminant".
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