Cancellations in Short Sums related to Hecke-Cusp Forms

Date of Submission

4-1-2024

Date of Award

10-1-2024

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Statistics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)

Supervisor

Munshi, Ritabrata (TSMU-Kolkata; ISI)

Abstract (Summary of the Work)

In number theory, a problem which arises in a variety of contexts is getting non- trivial cancellation for the general correlation problem, specially when we assume that they are short sums related to Hecke-cusp forms. In my thesis, I have studied the cancellation range for those short sums where they have non-trivial bounds. For these problems, we have used the delta method which was developed by Prof. Ritabrata Munshi in his famous circle method papers. I have studied the delta method in the first chapter of the thesis where the reader will get a notion about the structure of the delta method. In the second and third chapter, I have improved the well-known cancellation range for the short sums related to GL(1) twists of GL(2) Hecke-cusp forms and got significant ranges, without going through the theory of L-functions. In the last chapter, I have studied a subconvexity problem, which, after applying the approximate functional equation, boils down to short sums.

Comments

ProQuest Collection ID: https://www.proquest.com/pqdtlocal1010185/dissertations/fromDatabasesLayer?accountid=27563

Control Number

ISILib-TH

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DSpace Identifier

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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