Weber's class invariants revisited
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Publication:1396451
DOI10.5802/jtnb.361zbMath1022.11056OpenAlexW2028193830MaRDI QIDQ1396451
Publication date: 30 June 2003
Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=JTNB_2002__14_1_325_0
Quadratic extensions (11R11) Modular and automorphic functions (11F03) Complex multiplication and moduli of abelian varieties (11G15) Class field theory (11R37) Dedekind eta function, Dedekind sums (11F20)
Related Items (24)
Singular moduli of \(r\)th roots of modular functions ⋮ On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono ⋮ Explicit computations in Iwasawa theory ⋮ Modularity of Galois traces of class invariants ⋮ Singular values of some modular functions ⋮ Computing Hilbert Class Polynomials ⋮ Computing the cardinality of CM elliptic curves using torsion points ⋮ Algebraic properties of the modular lambda function ⋮ An explicit factorization formula for the singular values of \(\varphi \) and the generalized principal ideal theorem ⋮ Class invariants for certain non-holomorphic modular functions ⋮ On the Computation of Class Polynomials with “Thetanullwerte” and Its Applications to the Unit Group Computation ⋮ Constructing elliptic curves over finite fields using double eta-quotients ⋮ Choosing the correct elliptic curve in the CM method ⋮ Efficient CM-constructions of elliptic curves over finite fields ⋮ The complexity of class polynomial computation via floating point approximations ⋮ Ramanujan's class invariants and their use in elliptic curve cryptography ⋮ On the efficient generation of prime-order elliptic curves ⋮ Point counting on reductions of CM elliptic curves ⋮ Short addition sequences for theta functions ⋮ Special values of hypergeometric functions over finite fields ⋮ Unnamed Item ⋮ Implementing the asymptotically fast version of the elliptic curve primality proving algorithm ⋮ Generalized class polynomials ⋮ Generalised Weber functions
Cites Work
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- Zur Theorie der Ringklassenkörper über imaginär-quadratischen Zahlkörpern
- Explicit elliptic units. I
- Construction of ray class fields by elliptic units
- On the `gap' in a theorem of Heegner
- Diophantine analysis and modular forms
- Über einige Anwendungen Dedekindscher Summen.
- Die singulären Werte der Weberschen Funktionen f, f1, f2, 2, 3.
- Bemerkungen zum Satz von Heegner-Stark über die imaginär-quadratischen Zahlkörper mit der Klassenzahl Eins.
- Weber's class invariants
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