Siegel modular cusp forms of degree two
نویسندگان
چکیده
منابع مشابه
On Level p Siegel Cusp Forms of Degree Two
In the previous paper 1 , the second and the third authors introduced a simple construction of a Siegel cusp form of degree 2. This construction has an advantage because the Fourier coefficients are explicitly computable. After this work was completed, Kikuta and Mizuno proved that the p-adic limit of a sequence of the aforementioned cusp forms becomes a Siegel cusp form of degree 2 with level ...
متن کاملTransfer of Siegel Cusp Forms of Degree 2
Let π be the automorphic representation of GSp4(A) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and τ be an arbitrary cuspidal, automorphic representation of GL2(A). Using Furusawa’s integral representation for GSp4 ×GL2 combined with a pullback formula involving the unitary group GU(3, 3), we prove that the L-functions L(s, π× τ ) are “nice”. The conve...
متن کاملRamanujan - type results for Siegel cusp forms of degree 2
A result of Chai–Faltings on Satake parameters of Siegel cusp forms together with the classification of unitary, unramified, irreducible, admissible representations of GSp4 over a p-adic field, imply that the local components of the automorphic representation of GSp4 attached to a cuspidal Siegel eigenform of degree 2 must lie in certain families. Applications include estimates on Hecke eigenva...
متن کاملShifted products of Fourier coefficients of Siegel cusp forms of degree two
Let f be an elliptic cusp form of integral weight k on a congruence subgroup of Γ1 := SL2(Z) with real Fourier coefficients a(n)(n ≥ 1). Let r be a fixed positive integer. Then it was proved in [5] that the sequence (a(n)a(n + r))n≥1 has infinitely many nonnegative as well as infinitely many non-positive terms. The proof essentially is based on a sign-change result for the Fourier coefficients ...
متن کاملOn the graded ring of Siegel modular forms of degree
The aim of this paper is to give the dimension of the space of Siegel modular forms M k (Γ(3)) of degree 2, level 3 and weight k for each k. Our main result is Theorem dim M k (Γ(3)) = 1 2 (6k 3 − 27k 2 + 79k − 78) k ≥ 4. In other words we have the generating function : ∞ k=0 dim M k (Γ(3))t k = 1 + t + t 2 + 6t 3 + 6t 4 + t 5 + t 6 + t 7 (1 − t) 4. About the space of cusp forms, the dimension ...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1981
ISSN: 0040-8735
DOI: 10.2748/tmj/1178229494