## Experimental Mathematics

- Experiment. Math.
- Volume 6, Issue 1 (1997), 57-76.

### On the Hasse-Witt invariants of modular curves

Pilar Bayer and Josep González

#### Abstract

We briefly discuss the relationship between several characterizations of the Hasse--Witt invariant of curves in characteristic $p$ with the goal of computing its value in concrete instances. We study its asymptotic behaviour when dealing with the geometric fibres of curves of genus $\geq 2$ defined over the rationals. Numerical evidence gathered for several modular curves supports certain conjectural distribution laws.

#### Article information

**Source**

Experiment. Math. Volume 6, Issue 1 (1997), 57-76.

**Dates**

First available in Project Euclid: 13 March 2003

**Permanent link to this document**

http://projecteuclid.org/euclid.em/1047565284

**Mathematical Reviews number (MathSciNet)**

MR1464582

**Zentralblatt MATH identifier**

0923.11090

**Subjects**

Primary: 11G10: Abelian varieties of dimension > 1 [See also 14Kxx]

Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35] 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]

#### Citation

Bayer, Pilar; González, Josep. On the Hasse-Witt invariants of modular curves. Experiment. Math. 6 (1997), no. 1, 57--76. http://projecteuclid.org/euclid.em/1047565284.