The Manin-Drinfeld theorem and Ramanujan sums

DOI10.1007/BF02837828zbMath0671.14013OpenAlexW2004556724MaRDI QIDQ1119705

V. Kumar Murty, Dinakar Ramakrishnan

Publication date: 1987

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02837828

zbMATH Keywords

Fourier coefficientsmodular curveRamanujan sumsnumber of divisorsFermat curvecuspidal divisor

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Holomorphic modular forms of integral weight (11F11) Global ground fields in algebraic geometry (14G25)

Related Items (6)

The unbounded denominators conjecture for the noncongruence subgroups of index 7 ⋮ The minimal regular model of a Fermat curve of odd squarefree exponent and its dualizing sheaf ⋮ The Eisenstein cycles and Manin-Drinfeld properties ⋮ The Manin-Drinfeld theorem and the rationality of Rademacher symbols ⋮ The spectrum of Fermat curves ⋮ Néron-Tate heights on algebraic curves and subgroups of the modular group

Cites Work

• Arithmetic on modular curves
• Points at infinity on the Fermat curves
• Gamma function identities and elliptic differentials on Fermat curves
• Two theorems on modular curves
• A regulator for curves via the Heisenberg group
• Fourier coefficients of Eisenstein series on non-congruence subgroups
• On Elliptic Curves with Complex Multiplication as Factors of the Jacobians of Modular Function Fields
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