On zeros of fractional derivatives of Dirichlet series and polynomials
- UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
- Torre Eugene Caparatta (Creator)
- Institution
- The University of North Carolina at Greensboro (UNCG )
- Web Site: http://library.uncg.edu/
- Advisor
- Sebastian Pauli
Abstract: In this thesis we apply some of the important concepts of Complex Analysis and Fractional Calculus to several special functions from Analytic Number Theory. For Euler eta, Dirichlet L-functions and polynomials we establish new zero-free regions and explore the paths of zeros of their fractional derivatives, using our algorithms for their evaluation. We also consider the number of zeros of integral derivatives for Euler eta function and the behavior of fractional Stieltjes constants of eta and Dirichlet L-functions. Most of these results extend classical theorems concerning integral derivatives of these functions and lead to a better understanding of the general theory.
On zeros of fractional derivatives of Dirichlet series and polynomials
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Created on 5/1/2024
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Additional Information
- Publication
- Dissertation
- Language: English
- Date: 2024
- Keywords
- Complex Analysis, Dirichlet Series, Fractional Calculus, Polynomials
- Subjects
- Dirichlet series
- Polynomials
- Fractional calculus
- Functions of complex variables