Explicit calculations with Eisenstein series

By M. Young. Journal of Number Theory, 2017

62 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a4067771738fbe7c812be5492127c2da2f219333

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In Algebra and Number Theory

1. Ian Petrow
2. M. Young
3. Siegfred Baluyot
4. Stephan Baier
5. Manjul Bhargava
6. A. Shankar
7. Alexandra Florea

In Geometry and Topology

1. Ian Petrow
2. M. Young

In Mathematical Physics

1. Ian Petrow
2. M. Young
3. Alexandra Florea

Citations in the corpus

• The fourth moment of Dirichlet L-functions along a coset and the Weyl bound (2019, unknown): “where the notation matches that in [Y2].”
• A generalized cubic moment and the Petersson formula for newforms (2016, methodology): “ setting of the BruggemanKuznetsov formula, then our methods should carry over to the Maass case, as in [CI]. Note added May 31, 2018: the Bruggeman-Kuznetsov formula for newforms has now appeared in [Y2]. The type of sum appearing in Theorem 1.1 may look somewhat unusual, but it is very important f”