What is knowns about Weierstrass points on modular curves? Are there any explicit formulas of them, or any information about Weierstrass gaps? I am interested in (compactifications of) the quotients of the upper half plane by $\Gamma(n)$, $\Gamma_1(n)$ or $\Gamma_0(n)$. The level $n$ may be assumed to be prime, if that helps.


You might try google or MathSciNet yourself before asking on MathOverflow. It took 1 minute to find the following three articles:

MR2059755 (2006b:11056) Ahlgren, Scott . The arithmetic of Weierstrass points on modular curves X0(p). Galois theory and modular forms, 3--12, Dev. Math., 11, Kluwer Acad. Publ., Boston, MA, 2004.

MR1962053 (2004b:11086) Ahlgren, Scott ; Ono, Ken . Weierstrass points on X0(p) and supersingular j-invariants. Math. Ann. 325 (2003), no. 2, 355--368.

MR1946403 (2003j:11065) Ahlgren, Scott ; Papanikolas, Matthew . Higher Weierstrass points on X0(p). Trans. Amer. Math. Soc. 355 (2003), no. 4, 1521--1535 (electronic).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.