On mod p singular modular forms
نویسندگان
چکیده
منابع مشابه
SIEGEL MODULAR FORMS ( MOD p ) AND ALGEBRAIC MODULAR FORMS
In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...
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We prove many cases of a conjecture of Buzzard, Diamond and Jarvis on the possible weights of mod p Hilbert modular forms, by making use of modularity lifting theorems and computations in p-adic Hodge theory.
متن کاملHecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms
In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...
متن کاملUPPER BOUND ON THE NUMBER OF SYSTEMS OF HECKE EIGENVALUES FOR SIEGEL MODULAR FORMS (MOD p)
. The constants are effectively computable. Proof. Part (a) follows from the fact that the algebraic group GSp2g has dimension 2g +g+1. Part (b) is obvious. Combined with Theorem 1.1 of [Ghi04], Theorem 1 gives Corollary 3 (Algebraic modular forms). Let B/Q be the quaternion algebra ramified at p and ∞. The number of systems of Hecke eigenvalues coming from algebraic modular forms (mod p) of le...
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Complex dynamical systems on the Riemann sphere do not possess " invariant forms ". However there exist non-trivial examples of dynamical systems, defined over number fields, satisfying the property that their reduction modulo ℘ possesses " invariant forms " for all but finitely many places ℘. The paper completely characterizes those dynamical systems possessing the latter property. 1. Motivati...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2016
ISSN: 0933-7741,1435-5337
DOI: 10.1515/forum-2015-0062