Explicit calculations with Eisenstein series

Matthew P Young

doi:10.1016/j.jnt.2018.11.007

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arXiv · 1710.03624

Explicit calculations with Eisenstein series

Matthew P Young

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Abstract

We find explicit change-of-basis formulas between Eisenstein series attached to cusps, and newform Eisenstein series attached to pairs of primitive Dirichlet characters. As a consequence, we prove a Bruggeman-Kuznetsov formula for newforms of square-free level and trivial nebentypus. We also derive, in explicit form, the Fourier expansion, Hecke eigenvalues, Atkin-Lehner pseudo-eigenvalues, and other data associated to these Eisenstein series, with arbitrary integer weight, level, and nebentypus.

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Matthew P Young. 2017-11-03. Explicit calculations with Eisenstein series. https://doi.org/10.1016/j.jnt.2018.11.007

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