On the genera of X_0(N)
Abstract
Let g_0(N) be the genus of the modular curve X_0(N). We record several properties of the sequence {g_0(N)}. Even though the average size of g_0(N) is 1.25N/pi^2, a random positive integer has probability zero of being a value of g_0(N). Also, if N is a random positive integer then g_0(N) is odd with probability one. The smallest non-negative integer not occuring as g_0(N) for any N is 150; the smallest such odd integer is 49267.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 2000
- DOI:
- 10.48550/arXiv.math/0006096
- arXiv:
- arXiv:math/0006096
- Bibcode:
- 2000math......6096C
- Keywords:
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- Number Theory;
- Algebraic Geometry;
- 14G35
- E-Print:
- 9 pages