A Li-type criterion for zero-free half-planes of Riemann's zeta function
Abstract
We define a sequence of real functions which coincide with Li's coefficients at one and which allow us to extend Li's criterion for the Riemann Hypothesis to yield a necessary and sufficient condition for the existence of zero-free strips inside the critical strip $0<\Re(z)<1$. We study some of the properties of these functions, including their oscillatory behaviour.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- July 2005
- DOI:
- 10.48550/arXiv.math/0507368
- arXiv:
- arXiv:math/0507368
- Bibcode:
- 2005math......7368F
- Keywords:
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- Number Theory;
- 11M26;
- 11M06
- E-Print:
- 15 pages, to appear in the J. London Math. Soc