Riemann-von Mangoldt formula

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This lesson examines the Riemann-von Mangoldt formula, initially proposed by Riemann in his renowned work “On the Number of Primes Less Than a Given Quantity”. It was rigorously proven by von Mangoldt in 1905.

The formula calculates the number N(T) of zeros of the Zeta Function within the critical strip, specifically those that have an imaginary part t ranging from 0 to T.

The paper by von Mangoldt is among the earliest discussing the function N(T) and its related topics, which remain an active area of modern research.

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