Riemann Zeta Function: Exploring the World of Number Theory
What are some inputs and outputs for the Riemann Zeta function?
Let's delve into the fascinating realm of complex-valued functions with the Riemann Zeta function. What are some examples of inputs and their corresponding outputs for this intriguing function?
Inputs and Outputs for the Riemann Zeta function:
The Riemann Zeta function, ζ(s), is a complex-valued function with inputs and outputs such as s = 2 outputs ζ(2) = π²/6 ≈ 1.6449. It plays a crucial role in Number Theory, and is linked with the unsolved Riemann Hypothesis, which deals with the zeros of the function.
The Riemann Zeta function ζ(s) is a complex-valued function with one complex argument, which is traditionally represented as a real number x and an imaginary part y (s = x + iy). Here are some inputs and their respective outputs for the Riemann Zeta function:
- For s = 2, ζ(2) = π²/6 ≈ 1.6449
- For s = 4, ζ(4) = π⁴/90 ≈ 1.08232
- For s = 0, ζ(0) = -1/2
The Riemann Zeta function is also significant for its application in Number Theory and for the unsolved problem in mathematics, known as the Riemann Hypothesis, which says all nontrivial zeros of the Zeta function have real part equal to 1/2.