منابع مشابه
On a Result of Atkin and Lehner
We wish to give a new proof of one of the main results of Atkin-Lehner [1]. That paper depends, among other things, on a slightly strengthened version of Theorem 1 below, which characterizes forms in Sk(Γ0(N)) whose Fourier coefficients satisfy a certain vanishing condition. Our proof involves rephrasing this vanishing condition in terms of representation theory; this, together with an elementa...
متن کاملOn Atkin-lehner Quotients of Shimura Curves
We study the Čerednik-Drinfeld p-adic uniformization of certain AtkinLehner quotients of Shimura curves over Q. We use it to determine over which local fields they have rational points and divisors of a given degree. Using a criterion of Poonen and Stoll we show that the Shafarevich-Tate group of their jacobians is not of square order for infinitely many cases. In [PSt] Poonen and Stoll have sh...
متن کاملRational Points on Atkin-Lehner Quotients of Shimura Curves
We study three families of Atkin-Lehner quotients of quaternionic Shimura curves: X, X 0 (N), and X D+ 1 (N), which serve as moduli spaces of abelian surfaces with potential quaternionic multiplication (PQM) and level N structure. The arithmetic geometry of these curves is similar to, but even richer than, that of the classical modular curves. Two important differences are the existence of a no...
متن کاملOn Atkin-Lehner correspondences on Siegel spaces
We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime l...
متن کاملA mod ` Atkin-Lehner theorem and applications
If f(z) is a weight k ∈ 1 2 Z meromorphic modular form on Γ0(N) satisfying f(z) = ∑
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1992
ISSN: 0022-314X
DOI: 10.1016/0022-314x(92)90043-o