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The Manin—Drinfeld theorem and Ramanujan sums |
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| Authors: | V Kumar Murty Dinakar Ramakrishnan |
| Institution: | (1) Department of Mathematics, University of Toronto, M5S 1A1 Toronto, Ontario, Canada;(2) Department of Mathematics, Duke University, 27706 Durham, NC, USA;(3) Cornell University, 14853 Ithaca, NY, USA |
| Abstract: | The Manin—Drinfeld theorem asserts the finiteness of the cuspidal divisor class group of a modular curve corresponding to a congruence subgroup. The purpose of the note is to draw attention to the connection between this theorem and Ramanujan sums, and to the question of what happens for non-congruence subgroups. Research partially supported by an NSERC grant. Alfred P Sloan Fellow. Research partially supported by the NSF. |
| Keywords: | Modular curve cuspidal class group Eisenstein series Ramanujan sums non-congruence subgroups |
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