The cuspidal class number formula for the modular curves \(X_ 0(M)\) with \(M\) square-free

DOI10.1006/jabr.1996.6993zbMath0888.11021OpenAlexW2049500663MaRDI QIDQ1364264

Toshikazu Takagi

Publication date: 7 June 1998

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

Full work available at URL: https://doi.org/10.1006/jabr.1996.6993

zbMATH Keywords

modular curvesDedekind eta-functiondivisorscuspidal class number formulaanalog of Stickelberger idealgroup of modular units

Mathematics Subject Classification ID

Special algebraic curves and curves of low genus (14H45) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Elliptic and modular units (11G16)

Related Items (15)

On Eisenstein ideals and the cuspidal group of \(J_{0}(N)\) ⋮ On some arithmetic properties of Siegel functions ⋮ The rational torsion subgroups of Drinfeld modular Jacobians and Eisenstein pseudo-harmonic cochains ⋮ The rational cuspidal subgroup of J0(p2M)$J_0(p^2M)$ with M squarefree ⋮ The rational torsion subgroup of \(J_0(N)\) ⋮ 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 \(J_{1}(2p)\) ⋮ Unnamed Item ⋮ The cuspidal class number formula for certain quotient curves of the modular curve \(X_0(M)\) by Atkin-Lehner involutions ⋮ Modular units and cuspidal divisor class groups of \(X_1(N)\) ⋮ The cuspidal class number formula for the modular curves \(X_1(2p)\) ⋮ The rational cuspidal divisor class group of \(X_0(N)\) ⋮ THE JACQUET–LANGLANDS CORRESPONDENCE AND THE ARITHMETIC RIEMANN–ROCH THEOREM FOR POINTED CURVES ⋮ Eisenstein ideals and the rational torsion subgroups of modular Jacobian varieties. II.

Cites Work

• Unnamed Item
• Unnamed Item
• A cuspidal class number formula for the modular curves \(X_1(N)\)
• Cuspidal class number formula for the modular curves \(X_ 1(p)\)
• The index of Stickelberger ideals of order 2 and cuspidal class numbers
• The cuspidal class number formula for the modular curves \(X_ 1(p^ m)\)
• Two theorems on modular curves
• The cuspidal class number formula for the modular curves \(X_ 1(3^ m)\)
• Construction and Application of a Class of Modular Functions†
• Construction and Application of a Class of Modular Functions (II)†
• PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES

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