Triple Shifted Sums of Automorphic L-functions

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Overview

Title
Triple Shifted Sums of Automorphic L-functions
Contributors
Hulse, Thomas Andrew (creator)
Hoffstein, Jeffrey (Director)
Lee, Min (Reader)
Diaconu, Adrian (Reader)
Brown University. Mathematics (sponsor)
Copyright Date
2013
Abstract
In this work we provide a meromorphic continuation in three complex variables of two types of triple shifted convolution sums of Fourier coefficients of holomorphic cusp forms. The foundations of this construction are based in the continuation of the spectral expansion of a special truncated Poincaré series recently developed by Jeffrey Hoffstein. As a result we are able to produce previously unstudied and nontrivial asymptotics of truncated shifted sums which we expect to correspond to off-diagonal terms in the third moment of automorphic L-functions.
Keywords
spectral expansion
Maass forms
Automorphic forms
L-functions
Number theory
Notes
Thesis (Ph.D. -- Brown University (2013)
Extent
6, 86 p.

Citation

Hulse, Thomas Andrew, "Triple Shifted Sums of Automorphic L-functions" (2013). Mathematics Theses and Dissertations. Brown Digital Repository. Brown University Library. https://repository.library.brown.edu/studio/item/bdr:320605/

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