Cuspidal class number formula for the modular curves \(X_ 1(p)\)

DOI10.1016/0021-8693(92)90119-7zbMath0773.11040OpenAlexW2015817158MaRDI QIDQ1208092

Toshikazu Takagi

Publication date: 16 May 1993

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(92)90119-7

zbMATH Keywords

modular curvecuspidal class numberindex of a Stickelberger ideal

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35)

Related Items (11)

The cuspidal class number formula for the modular curves \(X_ 0(M)\) with \(M\) square-free ⋮ Determinantal formula for the cuspidal class number of the modular curve \(X_1(m)\) ⋮ The rational cuspidal subgroup of J0(p2M)$J_0(p^2M)$ with M squarefree ⋮ Modular units and cuspidal divisor classes on \(X_0(n^2M)\) with \(n|24\) and \(M\) squarefree ⋮ The cuspidal class number formula for the modular curves \(X_1(2^{2n+1})\) ⋮ The \(\mathbb{Q}\)-rational cuspidal group of \(J_{1}(2p)\) ⋮ Sporadic cubic torsion ⋮ The cuspidal class number formula for certain quotient curves of the modular curve \(X_0(M)\) by Atkin-Lehner involutions ⋮ A divisor formula and a bound on the \(\mathbb{Q} \)-gonality of the modular curve \(X_1(N)\) ⋮ The cuspidal class number formula for the modular curves \(X_1(2p)\) ⋮ Un crit\`ere d'\'epointage des sections $l$-adiques

Cites Work

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• Classification of normal congruence subgroups of G(\(\sqrt{q})\). II
• A cuspidal class number formula for the modular curves \(X_1(N)\)
• Units in the modular function field. I. - II: A full set of units. - III: Distribution relations
• Quadratic relations for units in the modular function field
• Distributions on toroidal groups
• Units in the modular function field. IV: The Siegel functions are generators
• The p-primary component of the cuspidal divisor class group on the modular curve X(p)
• The index of Stickelberger ideals of order 2 and cuspidal class numbers
• Two theorems on modular curves
• Bestimmung der Kommensurabilitätsklasse der Hilbertschen Modulgruppe
• On the Commensurability Class of the Rational Modular Group
• PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES

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