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ETH Zürich

1. Jana, Subhajit. Analytic Newvectors for GL(n,R) and Applications.

Degree: 2020, ETH Zürich

URL: http://hdl.handle.net/20.500.11850/418883

We introduce an analytic archimedean analogue of some aspects of the classical non-archimedean newvector theory formulated by Casselman and Jacquet – Piatetski-Shapiro – Shalika. We relate the analytic conductor of a generic irreducible representation of GL(n,R) to the invariance properties of some special vectors in that representation, which we name analytic newvectors.
We also provide a few natural applications of analytic newvectors to some analytic questions concerning automorphic forms for GL(n,Z) in the archimedean analytic conductor aspect. We prove an orthogonality result of the Fourier coefficients, a density estimate for the non-tempered forms, an equidistribution result for the Satake parameters with respect to the Sato – Tate measure, as well as a second moment estimate for the central L-values as strong as Lindeloef on average. We also verify the random matrix prediction concerning the distribution of the low-lying zeros of the Langlands L-functions in the analytic conductor aspect.
*Advisors/Committee Members: Nelson, Paul D., Michel, Philippe.*

Subjects/Keywords: Newvector; L-function; Automorphic forms; Whittaker functions; info:eu-repo/classification/ddc/510; Mathematics

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APA (6^{th} Edition):

Jana, S. (2020). Analytic Newvectors for GL(n,R) and Applications. (Doctoral Dissertation). ETH Zürich. Retrieved from http://hdl.handle.net/20.500.11850/418883

Chicago Manual of Style (16^{th} Edition):

Jana, Subhajit. “Analytic Newvectors for GL(n,R) and Applications.” 2020. Doctoral Dissertation, ETH Zürich. Accessed August 11, 2020. http://hdl.handle.net/20.500.11850/418883.

MLA Handbook (7^{th} Edition):

Jana, Subhajit. “Analytic Newvectors for GL(n,R) and Applications.” 2020. Web. 11 Aug 2020.

Vancouver:

Jana S. Analytic Newvectors for GL(n,R) and Applications. [Internet] [Doctoral dissertation]. ETH Zürich; 2020. [cited 2020 Aug 11]. Available from: http://hdl.handle.net/20.500.11850/418883.

Council of Science Editors:

Jana S. Analytic Newvectors for GL(n,R) and Applications. [Doctoral Dissertation]. ETH Zürich; 2020. Available from: http://hdl.handle.net/20.500.11850/418883