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Effective estimates for sums of Kloosterman sums, modular forms, and applications
Gonzalez-Pagan, Oscar E
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https://hdl.handle.net/2142/120190
Description
- Title
- Effective estimates for sums of Kloosterman sums, modular forms, and applications
- Author(s)
- Gonzalez-Pagan, Oscar E
- Issue Date
- 2023-01-05
- Director of Research (if dissertation) or Advisor (if thesis)
- Ahlgren, Scott
- Doctoral Committee Chair(s)
- Ahlgren, Scott
- Ford, Kevin
- Committee Member(s)
- Thorner, Jesse
- Zaharescu, Alexandru
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- Number Theory
- Modular Forms
- Kloosterman Sums
- Abstract
- In this thesis we explore applications of effective estimates for sums of Kloosterman sums, and consider some problems related to modular forms. In Chapter 1 we give a substantial improvement for the error term in the asymptotic formula for the smallest parts function spt(n) of Andrews. Our methods depend on an explicit bound for sums of Kloosterman sums of half integral weight. In the next chapter we establish an asymptotic formula with an effective bound on the error term for traces of singular moduli. The third chapter establishes the irreducibility of a family of polynomials associated to the zeros of Eisenstein series on SL2(Z). The final chapter provides a result about the factorization of the determinants of certain Hankel matrices related to Eisenstein series.
- Graduation Semester
- 2023-05
- Type of Resource
- Thesis
- Handle URL
- https://hdl.handle.net/2142/120190
- Copyright and License Information
- Copyright 2023 Oscar Gonzalez-Pagan
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