Galois groups via Atkin-Lehner twists
نویسندگان
چکیده
منابع مشابه
Galois Groups via Atkin-lehner Twists
Using Serre’s proposed complement to Shih’s Theorem, we obtain PSL2(Fp) as a Galois group over Q for at least 614 new primes p. Assuming that rational elliptic curves with odd analytic rank have positive rank, we obtain Galois realizations for 3 8 of the primes that were not covered by previous results; it would also suffice to assume a certain (plausible, and perhaps tractable) conjecture conc...
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These are the (more detailed) notes accompanying a talk that I am to give at the University of Pennsylvania on July 21, 2006. The topic is rational points on Atkin-Lehner twists of the modular curves X0(N). Apart from being an interesting Diophantine problem in its own right, there is an ulterior motive: Q-rational points correspond to “elliptic Q-curves” and thus to projective Galois represent...
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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 کاملBroué-Enguehard maps and Atkin-Lehner involutions
Let ` be one of the ten integers such that the sum of their divisors divide 24. For each such `, (except 15) we give a map from an algebra of polynomial invariants of some finite group to the algebra of modular forms invariant under the Atkin–Lehner group of level `. These maps are motivated and inspired by constructions of modular lattices from self-dual codes over rings. This work generalizes...
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) = ∑
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-06-08493-0