- #1
moriheru
- 273
- 17
How can one prove the above equation?
Thanks.
Thanks.
ζ(-1) is the value of the Riemann zeta function at -1. The Riemann zeta function is a mathematical function that is defined for complex numbers and is used to study the distribution of prime numbers.
The value of ζ(-1) being equal to -1/12 is a result of analytic continuation, which is a technique used to extend the domain of a mathematical function. In this case, the Riemann zeta function is extended to negative values, and the value at -1 is found to be -1/12.
Proving that ζ(-1) is equal to -1/12 is important because it has significant applications in physics and number theory. It is used in the calculation of Casimir force, which is a small attractive force between two uncharged parallel plates. It also has connections to the distribution of prime numbers and other important mathematical concepts.
The term "A Guide" in the title refers to the paper "Prove ζ(-1)=-1/12 - A Guide" written by Dr. Vijay Kumar, which provides a detailed and accessible explanation of the proof of ζ(-1)=-1/12. The paper serves as a guide for those interested in understanding the proof and its implications.
Yes, ζ(-1) is proven to be equal to -1/12 through rigorous mathematical proof. This result has been verified by multiple mathematicians and has been used in various applications. However, it should be noted that the value of -1/12 is a result of analytic continuation and does not hold for the original definition of the Riemann zeta function, which is only defined for values greater than 1.