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The Riemann Hypothesis: Zeros, Zeta, and Significance

Complex Analysis → Generalizations: L-functions and the Grand Riemann Hypothesis

This path guides graduate students through the mathematical foundations needed to understand the Riemann hypothesis, the distribution of nontrivial zeros of the Riemann zeta function, and its profound implications in number theory. It covers complex analysis, analytic number theory, and the prime number theorem, culminating in the statement and significance of the hypothesis.