Skip to Main Content
 

Global Search Box

 
 
 

ETD Abstract Container

Abstract Header

The Circle Method and Shifted Convolutions of Fourier Coefficients of Cusp Forms

Wei, Zhining
http://orcid.org/0000-0001-7541-3350
http://rave.ohiolink.edu/etdc/view?acc_num=osu168185485770591

Abstract Details

2023, Doctor of Philosophy, Ohio State University, Mathematics.
In my thesis, I will establish a power saving result for the shifted convolution sums of k-th powers and the normalized Fourier coefficients of cusp forms. Later I will generalize the result to higher rank cases. To prove the theorems, I will introduce the theory of automorphic forms, the standard circle method and some variants of the circle method. In the last chapter, I will move to Siegel cusp forms and study the linear relations of Siegel Poincare series. This will imply a non-vanishing result of the Fourier coefficients for Siegel-Hecke eigenforms. As a corollary, we can show a non-vanishing result of the central values of spinor functions associated to Siegel-Hecke eigenforms.
Wenzhi Luo (Advisor)
74 p.
Mathematics
Circle method, Fourier coefficients of cusp forms, Waring problem.

Recommended Citations

Citations

  • Wei, Z. (2023). The Circle Method and Shifted Convolutions of Fourier Coefficients of Cusp Forms [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu168185485770591

    APA Style (7th edition)

  • Wei, Zhining. The Circle Method and Shifted Convolutions of Fourier Coefficients of Cusp Forms. 2023. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu168185485770591.

    MLA Style (8th edition)

  • Wei, Zhining. "The Circle Method and Shifted Convolutions of Fourier Coefficients of Cusp Forms." Doctoral dissertation, Ohio State University, 2023. http://rave.ohiolink.edu/etdc/view?acc_num=osu168185485770591

    Chicago Manual of Style (17th edition)

osu168185485770591
130
© 2023, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.