The Zeta function, denoted by ζ(s), is a mathematical function that is defined for complex numbers s with real part greater than 1. It is defined as the sum of the reciprocals of the powers of positive integers raised to the s-th power. The Zeta function has many important properties and connections to number theory, complex analysis, and physics. One of its most famous properties is the Riemann Hypothesis, which states that all non-trivial zeros of the Zeta function have a real part of 1/2. **

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The Riemann zeta function has non-trivial zeros, which are complex numbers of the form \( s = \frac{1}{2} + it \), where \( t \) is a real number and \( i \) is the imaginary unit. These zeros are known as the non-trivial zeros because they do not lie on the real line. The Riemann Hypothesis states that all non-trivial zeros of the Riemann zeta function have a real part equal to \( \frac{1}{2} \), but this remains unproven. **

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