On the Atkin polynomials
نویسندگان
چکیده
منابع مشابه
On Atkin
In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the p-adic analogue of the threeterm recursion satisfied ...
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Schoof’s algorithm computes the number m of points on an elliptic curve E defined over a finite field Fq. Schoof determines m modulo small primes ` using the characteristic equation of the Frobenius of E and polynomials of degree O(`2). With the works of Elkies and Atkin, we have just to compute, when ` is a “good” prime, an eigenvalue of the Frobenius using polynomials of degree O(`). In this ...
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Let j be the modular invariant. For the primes p ≤ 23 the q-expansion coefficients of U(j− 744) are multiplicative as it was a Hecke eigenformmodulo a power of p which increases withm. This was conjectured by Atkin on the basis of extensive numerical experiments, and is proved in this paper. The cases p = 5, 7 and 11 are under special consideration in this paper.
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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 کاملOn 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...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2014
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2014.272.111