The zeta function is a complex function defined for complex numbers and plays a crucial role in number theory, especially in the distribution of prime numbers. It is often denoted as $$\zeta(s)$$, where $$s$$ is a complex variable. The function is intimately connected to the properties of arithmetic functions and provides deep insights into the Prime Number Theorem (PNT), linking the behavior of primes to the analytic properties of the zeta function in the complex plane.
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