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Riemann–von Mangoldt formula - Wikipedia

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In mathematics, the Riemann–von Mangoldt formula, named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt, describes the distribution of the zeros of the Riemann zeta function. The formula states that the number N(T) of zeros of the zeta function with imaginary part greater than 0 and less than or equal to T satisfies The formula was stated by Riemann in his notable paper "On the Number of Primes Less Than a Given Magnitude" (1859) and was finally proved by Mangoldt in 1905. Backlund gives an explicit form of the error for all T > 2: Under the Lindelöf and Riemann hypotheses the error term can be improved to 𝑜 ( log ⁡ 𝑇 ) and 𝑂 ( log ⁡ 𝑇 / log ⁡ log ⁡ 𝑇 ) respectively.[1] Similarly, for any primitive Dirichlet character χ modulo q, we have where N(T,χ) denotes the number of zeros of L(s,χ) with imaginary part between -T and T. This number theory-related article is a stub. You can help Wikipedia by expanding it.

Riemann–von Mangoldt formula - Wikipedia Jump to content From Wikipedia, the free encyclopedia This article includes a list of general references but lacks corresponding inline citations . Please help improve this article by introducing more precise citations. ( October 2019 ) ( Learn how and when to remove this message ) In mathematics , the Riemann–von Mangoldt formula , named for Bernhard Riemann and Hans Carl Friedrich von Mangoldt , describes the distribution of the zeros of the Riemann zeta function . The formula states that the number N ( T ) of zeros of the zeta function with imaginary

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