A supersingular congruence for modular forms
نویسندگان
چکیده
منابع مشابه
A Supersingular Congruence for Modular Forms
Let p > 3 be a prime. In the ring of modular forms with q-expansions defined over Z(p), the Eisenstein function Ep+1 is shown to satisfy (Ep+1) p−1 ≡ − −1 p ∆ 2−1)/12 mod (p, Ep−1). This is equivalent to a result conjectured by de Shalit on the polynomial satisfied by all the j-invariants of supersingular elliptic curves over Fp. It is also closely related to a result of Gross and Landweber use...
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We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.
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Let X35 be a Siegel cusp form of degree 2 and weight 35. Kikuta, Kodama and Nagaoka [4] proved that det T a(T, X35) ≡ 0 mod 23 for every half integral positive symmetric matrix T . In this paper, we give a finite number of examples of Hecke eigenforms of degree 2 and odd weights that have the same type of congruence relation above. We also introduce congruence relations for the Hecke eigenvalue...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1998
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-86-1-91-100