The zeta function is a special mathematical function that plays a critical role in number theory, particularly in understanding the distribution of prime numbers. It is most commonly associated with the Riemann zeta function, defined as $$ ext{ζ}(s) = rac{1}{2} + rac{1}{3^s} + rac{1}{4^s} + rac{1}{5^s} + ...$$ for complex numbers $$s$$ with real part greater than 1. The connections to prime numbers arise from its Euler product representation, linking it to the Prime Number Theorem and other significant results in number theory.
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