Arthur’s Truncated Eisenstein Series for SL(2, Z) and the Riemann Zeta Function: A Survey

Dorian Goldfeld ()
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Dorian Goldfeld: Columbia University, Mathematics Department

A chapter in Exploring the Riemann Zeta Function, 2017, pp 83-97 from Springer

Abstract: Abstract Eisenstein series are not in ℒ 2 $$\mathcal{L}^{2}$$ . Maass, and later Selberg, naively truncated the constant term of Eisenstein series (for symmetric spaces of rank 1) so that the resulting truncated Eisenstein series was square integrable. This procedure was generalized to Eisenstein series on higher rank groups by Langlands and Arthur. In this survey we focus on the deep connections between Eisenstein series for SL(2, Z), truncation, and the Riemann zeta function. Applications to zero free regions for the Riemann zeta function and automorphic L-functions are elucidated.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-59969-4_5

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DOI: 10.1007/978-3-319-59969-4_5

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