On the singular values of Weber modular functions

DOI10.1090/S0025-5718-97-00854-5zbMath0892.11022OpenAlexW2025384727WikidataQ61960122 ScholiaQ61960122MaRDI QIDQ4372640

Don Zagier, Noriko Yui

Publication date: 16 December 1997

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-97-00854-5

zbMATH Keywords

singular moduliWeber modular functionsfactorization of the discriminantGross-Zagier theoryroots of the class equationWeber's class equation

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Complex multiplication and moduli of abelian varieties (11G15) Class field theory (11R37) Elliptic and modular units (11G16)

Related Items (21)

Class invariants from a new kind of Weber-like modular equation ⋮ Three-variable Mahler measures and special values of \(L\)-functions of modular forms ⋮ Vertex operator algebras with central charge \(1/2\) and \(-68/7\) ⋮ Some non-congruence subgroups and the associated modular curves ⋮ Modularity of Galois traces of class invariants ⋮ There are at most finitely many singular moduli that are S-units ⋮ On a conjecture of Yui and Zagier ⋮ Characterization of the simple Virasoro vertex operator algebras with 2 and 3-dimensional space of characters ⋮ Constructing class invariants ⋮ Difference of modular functions and their CM value factorization ⋮ The Mahler measure of \((x+1/x)(y+1/y)(z+1/z)+\sqrt{k}\) ⋮ A nonsplit sum of coefficients of modular forms ⋮ Characters, supercharacters and Weber modular functions ⋮ Periodic points of algebraic functions and Deuring's class number formula ⋮ On the Evaluation of Singular Invariants for Canonical Generators of Certain Genus One Arithmetic Groups ⋮ A survey of computational class field theory ⋮ Class invariants by Shimura's reciprocity law ⋮ Some results in study of Kronecker limit formula and Dedekind sums ⋮ Difference of a hauptmodul for \(\Gamma_0 (N)\) and certain Gross-Zagier type CM value formulas ⋮ RAMANUJAN INVARIANTS FOR DISCRIMINANTS CONGRUENT TO 5 (mod 24) ⋮ An approach for computing generators of class fields of imaginary quadratic number fields using the Schwarzian derivative

Uses Software

• ECPP

Cites Work

• Explicit elliptic units. I
• Elliptic Curves and Primality Proving
• Die singulären Werte der Weberschen Funktionen f, f1, f2, 2, 3.
• Weber's class invariants
• Singular Moduli (3)^†
• Teilbarkeitseigenschaften der singulären Moduln der elliptischen Funktionen und die Diskriminante der Klassengleichung
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