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ETH Zürich

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

Degree: 2020, ETH Zürich

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 · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th 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 (16th Edition):

Jana, Subhajit. “Analytic Newvectors for GL(n,R) and Applications.” 2020. Doctoral Dissertation, ETH Zürich. Accessed August 05, 2020. http://hdl.handle.net/20.500.11850/418883.

MLA Handbook (7th Edition):

Jana, Subhajit. “Analytic Newvectors for GL(n,R) and Applications.” 2020. Web. 05 Aug 2020.

Vancouver:

Jana S. Analytic Newvectors for GL(n,R) and Applications. [Internet] [Doctoral dissertation]. ETH Zürich; 2020. [cited 2020 Aug 05]. 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

2. LI NING. INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS.

Degree: 2019, National University of Singapore

Subjects/Keywords: degenerate principal series; associated cycles; wave front cycles; the space of generalized Whittaker models; Kostant-Sekiguchi correspondence

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

NING, L. (2019). INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS. (Thesis). National University of Singapore. Retrieved from https://scholarbank.nus.edu.sg/handle/10635/162745

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

NING, LI. “INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS.” 2019. Thesis, National University of Singapore. Accessed August 05, 2020. https://scholarbank.nus.edu.sg/handle/10635/162745.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

NING, LI. “INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS.” 2019. Web. 05 Aug 2020.

Vancouver:

NING L. INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS. [Internet] [Thesis]. National University of Singapore; 2019. [cited 2020 Aug 05]. Available from: https://scholarbank.nus.edu.sg/handle/10635/162745.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

NING L. INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS. [Thesis]. National University of Singapore; 2019. Available from: https://scholarbank.nus.edu.sg/handle/10635/162745

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.