Weber's class invariants

DOI10.1112/S0025579300008251zbMath0226.12005MaRDI QIDQ5632668

B. J. Birch

Publication date: 1969

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

GaussHeegnerBakerStark10th discriminant problemRamachandra

Mathematics Subject Classification ID

Class field theory (11R37) Class numbers, class groups, discriminants (11R29)

Related Items (30)

Hilbert class polynomials and traces of singular moduli ⋮ Class invariants from a new kind of Weber-like modular equation ⋮ Three-variable Mahler measures and special values of \(L\)-functions of modular forms ⋮ Some Identities on the Character Sum Containing x(x - 1)(x - λ) ⋮ Weber's class invariants revisited ⋮ Applications of the theory of modular forms to number theory ⋮ Modularity of Galois traces of class invariants ⋮ The Mahler measure of x + 1/x + y + 1/y + 4 ± 42 and Beilinson’s conjecture ⋮ Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations ⋮ On a conjecture of Yui and Zagier ⋮ Mock Heegner points and congruent numbers ⋮ Computing the cardinality of CM elliptic curves using torsion points ⋮ Elliptic Curves and Primality Proving ⋮ Three constructions of rational points on \(Y^ 2=X^ 3\pm NX\) ⋮ On the singular values of Weber modular functions ⋮ The Mahler measure of \((x+1/x)(y+1/y)(z+1/z)+\sqrt{k}\) ⋮ EXPLICIT EVALUATIONS OF TWO RAMANUJAN–SELBERG CONTINUED FRACTIONS ⋮ Explicit evaluations of a Ramanujan-Selberg continued fraction ⋮ On the Computation of Class Polynomials with “Thetanullwerte” and Its Applications to the Unit Group Computation ⋮ Continued fractions and modular functions ⋮ Choosing the correct elliptic curve in the CM method ⋮ Arithmetische Ausdeutung der Klassenzahlformel für einfach reelle kubische Zahlkörper ⋮ Arithmetic on algebraic varieties ⋮ A genus two curve related to the class number one problem ⋮ Class invariants by Shimura's reciprocity law ⋮ Unnamed Item ⋮ Nombres de Hurwitz et unités elliptiques. Un critère de régularité pour les extensions abéliennes d'un corps quadratique imaginaire ⋮ Point counting on reductions of CM elliptic curves ⋮ Generalized class polynomials ⋮ Generalised Weber functions

Cites Work

• Zur komplexen Multiplikation
• Some applications of Kronecker's limit formulas
• A complete determination of the complex quadratic fields of class-number one
• Imaginäre quadratische Zahlkörper mit der Klassenzahl Eins
• On the proof of Stark's theorem
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• Diophantine analysis and modular forms
• Zum Hauptidealsatz der komplexen Multiplikation
• Singular Moduli (6)

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