On the Motion of Zeros of Zeta Functions

Details On the Motion of Zeros of Zeta Functions On the Motion of Zeros of Zeta Functions

2001-02-08

arxiv.org/abs/math-ph/0102007v1

Physics

Mathematical Physics

11 pages, 3 figures (better image resolution available on http://www.msi.vxu.se/~sgo)

Scientific paper

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which are linear combinations of different Hurwitz zeta functions, and have a symmetric distribution of their zeros with respect to the critical line, are examined. Finally the existence of the hypothetical non-trivial Riemann zeros with $Re(s)\neq 1/2$ is discussed.

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