Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weightsTools Neururer, Michael (2016) Products of Eisenstein series, their L-functions, and Eichler cohomology for arbitrary real weights. PhD thesis, University of Nottingham.
AbstractOne topic of this thesis are products of two Eisenstein series. First we investigate the subspaces of modular forms of level N that are generated by such products. We show that of the weight k is greater than 2, for many levels, one can obtain the whole of M[subspace]k(N) from Eisenstein series and products of two Eisenstein series. We also provide a result in the case k=2 and treat some spaces of modular forms of non-trivial nebentypus. We then analyse the L-functions of products of Eisenstein series. We reinterpret a method by Rogers-Zudilin and use it in two applications, the first concerning critical L-values of a product of two Eisenstein series, and the second special values of derivatives of L-functions.
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