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Title: Square roots of symplectic L-functions and Reidemeister torsion
Authors: Abdurrahman, Amina
Advisors: Venkatesh, Akshay
Contributors: Mathematics Department
Subjects: Mathematics
Issue Date: 2022
Publisher: Princeton, NJ : Princeton University
Abstract: We study the existence of a square root of a symplectic L-function. In joint work with A. Venkatesh we conjecture a global cohomological formula for the central value of a symplectic L-function up to squares, which in particular gives a criterion for the existence of a square root. Using ideas from arithmetic topology we formulate an analogous conjecture about the Reidemeister torsion of 3-manifolds up to squares. We give a proof of the topological statement in full generality and of the arithmetic statement under some assumptions. We note that the topological theorem is central in the proof of the arithmetic statement.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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