An Experimental Mathematics Approach to Truncated Riemann Zeta Function

An Experimental Mathematics Approach to Truncated Riemann Zeta Function
By
Edna L. Jones, Yukun Yao, and Doron Zeilberger
.pdf LaTeX source

Written: Jan.-Feb. 2019
Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

As a case study and class project of experimental mathematics, we implemented efficient programs to compute truncated Riemann Zeta functions and find minimums for the absolute value of Truncated Riemann Zeta Function. The details of programs and results are discussed. Future work may include approximation by continued fraction and the asymptotic estimates which are briefly mentioned here.
This paper presents a collection of experimental results regarding the truncated Riemann Zeta function conducted by students in Dr. Z.'s Spring 2018 Experimental Mathematics Class.

Accompanying Maple package is TruncatedRiemannZeta.txt.

Maple packages

TruncatedRiemannZeta.txt

Sample Output Files

Animation of the Truncated Riemann Zeta function for various N's
Picture of ZNt(5,t)
Picture of ZNtR(10,t)
Picture of AsyTRZ(100, t) for t from 100 to 200
Picture of AsyTRZ(100, t) for t from 500 to 5000
Picture of AsyTRZ(N, 100) for N from 100 to 500

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