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doctoral thesis

Algebraic twists of GL(2) automorphic forms

Nadarajan, Vignesh Arumugam  
2023

In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and includes many standard exponential sums including Gauss sums, Kloosterman sums, Hyperkloosterman sums etc. In particular we prove a Burgess type power saving (of exponent 1/8) over the trivial bound. This generalizes the results of [FKM15] to the case of number fields with a slightly more restrictive assumption on the automorphism group attached to the trace function. We work using the language of adeles which makes the analysis involved softer and makes the generalisation to number fields more natural. The proof proceeds by studying the amplified second moment spectral average of the correlation sum using the relative trace formula. This, like in the case of [FKM15] leads us to use square root cancellation of the autocorrelation sums of the trace function.

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Type
doctoral thesis
DOI
10.5075/epfl-thesis-10178
Author(s)
Nadarajan, Vignesh Arumugam  
Advisors
Michel, Philippe  
Jury

Prof. Friedrich Eisenbrand (président) ; Prof. Philippe Michel (directeur de thèse) ; Prof. Emmanuel Kowalski, Prof. Etienne Fouvry, Prof. Valentin Blomer (rapporteurs)

Date Issued

2023

Publisher

EPFL

Publisher place

Lausanne

Public defense year

2023-12-19

Thesis number

10178

Total of pages

71

Subjects

automorphic forms

•

trace functions

•

Hecke eigenvalues

•

relative trace formula

•

algebraic twists

•

subconvexity

EPFL units
TAN  
Faculty
SB  
School
MATHGEOM  
Doctoral School
EDMA  
Available on Infoscience
December 11, 2023
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/202560
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