How is it possible that the Riemann zeta function of all negative integers is 0. And why is it that zeta of -1 is the only non-zero value (-1/12)?
Does anyone have a good and/or intuitive explanation for it?
Asked
Active
Viewed 583 times
-1
-
John Baez's talk sheds some light on this, without much complex analysis. https://youtu.be/vzjbRhYjELo – John Molokach Jun 13 '15 at 19:26
1 Answers
1
The riemann zeta function equals zero for all even negative integers. These are known as the trivial zeros. If you do not know the underlying theory of the Riemann Zeta function / analytic continuation, it will be very difficult to offer an "intuitive" explanation for why.
MT_
- 19,603
- 9
- 40
- 81
-
Could you tell me what a good source is for learning about this topic? – Researcher_Witty Jun 13 '15 at 17:35
-
I wrote my master's thesis on this and many other aspects of the zeta function. http://thescholarship.ecu.edu/bitstream/handle/10342/4703/Molokach_ecu_0600O_11345.pdf?sequence=1&isAllowed=y – John Molokach Jun 13 '15 at 19:23