On the genera of X_0(N)
Number Theory
2007-05-23 v2 Algebraic Geometry
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.
Cite
@article{arxiv.math/0006096,
title = {On the genera of X_0(N)},
author = {János A. Csirik and Joseph L. Wetherell and Michael E. Zieve},
journal= {arXiv preprint arXiv:math/0006096},
year = {2007}
}
Comments
9 pages; minor changes in v2