On the genera of X_0(N)

J\'anos A. Csirik; Joseph L. Wetherell; Michael E. Zieve

arxiv: math/0006096 · v2 · submitted 2000-06-13 · 🧮 math.NT · math.AG

On the genera of X₀(N)

J\'anos A. Csirik , Joseph L. Wetherell , Michael E. Zieve This is my paper

classification 🧮 math.NT math.AG

keywords integerpositiveprobabilityrandomsmallestaveragecurveeven

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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.

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On the genera of X₀(N)

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