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Twisting of Siegel paramodular forms

Jennifer Johnson-Leung

http://orcid.org/0000-0001-8657-4192

Department of Mathematics, University of Idaho, Moscow, Idaho 83844, USA

E-mail Address: [email protected]

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and

Brooks Roberts

Department of Mathematics, University of Idaho, Moscow, Idaho 83844, USA

E-mail Address: [email protected]

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https://doi.org/10.1142/S1793042117501019Cited by:4 (Source: Crossref)

Abstract

Let S_k(Γ^para(N)) be the space of Siegel paramodular forms of level N and weight k. Fix an odd prime p ∤ N and let χ be a nontrivial quadratic Dirichlet character mod p. Based on [Twisting of paramodular vectors, Int. J. Number Theory10 (2014) 1043–1065], we define a linear twisting map 𝒯_χ : S_k(Γ^para(N)) → S_k(Γ^para(Np⁴)). We calculate an explicit expression for this twist, give the commutation relations of this map with the Hecke operators and Atkin–Lehner involution for primes ℓ ≠p, and prove that the L-function of the twist has the expected form.

Keywords:

AMSC: 11F46, 11F70

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