Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Thesis.pdf (518.23 KB)

ETD Abstract Container

Abstract Header

On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms

Ravindran, Hari Alangat
http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Mathematics.
The study of shifted convolution sums has acquired a prominent place in current number theory research owing to its potential applications to the sub-convexity problem, while quadratic forms have fascinated mathematicians since antiquity. This thesis, which deals with both these topics, studies shifted convolution sums involving the Fourier coefficients of Theta Series associated to a positive definite integral quadratic form and a cuspidal Hecke eigenform of integral weight. Our aim is to generalize the work of W. Luo, J. Hafner, and H. Iwaniec et al. in this new setting. Three independent approaches are used in this endeavour -- the spectral theory of the hyperbolic Laplacian, the δ-symbol method (a variant of the Hardy-Littlewood-Ramanujan circle method), and the theory of Poincaré series via a Poisson-Voronoï summation formula. We establish asymptotic formulae in all three aspects with the spectral theory approach providing the optimal estimate for the error term when one of the forms involved is cuspidal, while the δ-symbol method gives a sharp error term when only Theta Series are involved in the shifted convolution sum.
Wenzhi Luo, Dr. (Advisor)
Roman Holowinsky, Dr. (Committee Member)
Jeffery McNeal, Dr. (Committee Member)
Virginia Sanders, Dr. (Committee Member)
97 p.
Mathematics
Poisson-Voronoi summation formula; shifted convolution sum; quadratic forms; delta-symbol method

Recommended Citations

Citations

  • Ravindran, H. A. (2014). On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690

    APA Style (7th edition)

  • Ravindran, Hari. On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690.

    MLA Style (8th edition)

  • Ravindran, Hari. "On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690

    Chicago Manual of Style (17th edition)

osu1406039690
1,108
© 2014, some rights reserved.Creative Commons License On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms by Hari Alangat Ravindran is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.