منابع مشابه
Arithmetic of Certain Hypergeometric Modular Forms
In a recent paper, Kaneko and Zagier studied a sequence of modular forms Fk(z) which are solutions of a certain second order differential equation. They studied the polynomials e Fk(j) = Y τ∈H/Γ−{i,ω} (j − j(τ))τ k, where ω = e2πi/3 and H/Γ is the usual fundamental domain of the action of SL2(Z) on the upper half of the complex plane. If p ≥ 5 is prime, they proved that e Fp−1(j) (mod p) is the...
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We investigate certain finiteness questions that arise naturally when studying approximations modulo prime powers of p-adic Galois representations coming from modular forms. We link these finiteness statements with a question by K. Buzzard concerning p-adic coefficient fields of Hecke eigenforms. Specifically, we conjecture that for fixed N , m, and prime p with p not dividing N , there is only...
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By a combined use of analytical, algebraic and computational tools we derive a description of the algebra of modular forms with respect to a certain congruence subgroup of SL2(Z)× SL2(Z) of level 3. Mathematics Subject Classification: 11F55; 13A50, 20C40, 13P99.
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We introduce a differential operator invariant under the special linear group SL(2n, C), and, as a consequence, the symplectic group Sp(2n, C). Connections with generalized Rankin–Cohen brackets for Siegel modular forms of genus n are sketched.
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0. Introduction In [1], gravitational anomaly cancellation formulas are derived from direct computations. In particular, in dimension 12, the Alvarez-Gaumé and Witten ‘‘miraculous cancellation’’ formula can be written as {L(TX, ∇TX )}(12) = {8A(TX, ∇TX )ch(TCX, ∇TCX )}(12) − 32{A(TX, ∇TX )}(12), (0.1) where X is a twelve-dimensional Riemannian manifold, ∇TX is the associated Levi-Civita conn...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2010
ISSN: 0208-6573
DOI: 10.7169/facm/1285679143