Displaying similar documents to “Mixed automorphic forms and differential equations.”

Eisenstein series and Poincaré series for mixed automorphic forms.

Min Ho Lee (2000)

Collectanea Mathematica

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Mixed automorphic forms generalize elliptic modular forms, and they occur naturally as holomorphic forms of the highest degree on families of abelian varieties parametrized by a Riemann surface. We construct generalized Eisenstein series and Poincaré series, and prove that they are mixed automorphic forms.

Nonvanishing of automorphic L-functions at special points

Zhao Xu (2014)

Acta Arithmetica

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At some special points, we establish a nonvanishing result for automorphic L-functions associated to the even Maass cusp forms in short intervals by using the mollification technique.

K-finite Whittaker functions are of finite order one

(2013)

Acta Arithmetica

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We prove a finite order one type estimate for the Whittaker function attached to a K-finite section of a principle series representation of a real or complex Chevalley group. Effective computations are made using convexity in ℂⁿ, following the original paper of Jacquet. As an application, we give a simplified proof of the known result of the boundedness in vertical strips of certain automorphic L-functions, using a result of Müller.