riemann in A Sentence

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    Did you just solve Riemann?

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    The Riemann sphere.

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    German mathematician Bernard Riemann died of TB disease in 1866.

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    This work of Riemann later became fundamental for Einstein's theory of relativity.

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    Cramér proved that, assuming the Riemann hypothesis, every gap is O√p log p.

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    However, several of his students became influential mathematicians, among them Richard Dedekind and Bernhard Riemann.

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    The Riemann hypothesis discusses zeros outside the region of convergence of this series and Euler product.

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    For almost 160 years, the Riemann hypothesis has been one of mathematics most famous unsolved problems.

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    After? So, we see that the zeroes, of the Riemann zeta function, correspond to singularities, in space-time.

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    After? So, we see that the zeros of the Riemann zeta function correspond to singularities in space-time.

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    After? So, we see that the zeroes of the Riemann Zeta function… correspond to singularities… in space-time.

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    Von Koch(1901) proved that the Riemann hypothesis implies the"best possible" bound for the error of the prime number theorem.

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    After? So, we see that the zeroes of the Riemann Zeta function… correspond to singularities… in space-time… Singularities in space-time then.

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    The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics.

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    The Riemann hypothesis, along with the Goldbach conjecture, is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems.

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    Yesterday, a highly regarded mathematician claimed in a lecture that he has proven perhaps the most famous of these problems, called the Riemann hypothesis.

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    The Riemann zeta function ζ(s) is a function whose argument s may be any complex number other than 1, and whose values are also complex.

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    Of course, calculus turned out to be lucrative in a myriad of other domains too, but can we say the same thing about Riemann's Hypothesis?

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    On Monday, a highly regarded mathematician claimed in a lecture that he has proven perhaps the most famous of these problems, called the Riemann hypothesis.

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    In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2.

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    Consequences The practical uses of the Riemann hypothesis include many propositions known true under the Riemann hypothesis, and some that can be shown to be equivalent to the Riemann hypothesis.

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    Bernhard Riemann, a student of Gauss, had applied methods of calculus in a ground-breaking study of the intrinsic(self-contained) geometry of all smooth surfaces, and thereby found a different non-Euclidean geometry.

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    For instance, Riemann developed his absurd concepts of curved geometry in the 1850s, which seemed inapplicable until Einstein used them to rediscover the laws of gravity in his General Theory of Relativity.

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    The statement that the equation 1 ζ( s) ∑ n 1 ∞ μ( n) n s{\displaystyle{\frac{1}{\zeta( s)}}\ sum{ n=1}{\ infty}{\ frac{\ mu( n)}{ n{ s}}}} is valid for every s with real part greater than 1/2, with the sum on the right hand side converging, is equivalent to the Riemann hypothesis.

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    Riemann's explicit formula for the number of primes less than a given number in terms of a sum over the zeros of the Riemann zeta function says that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros of the zeta function.

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    A precise version of Koch 's result, due to Schoenfeld( 1976), says that the Riemann hypothesis implies π( x)- li( x) 1 8 π x log( x), for all x 2657,{\ displaystyle\ pi( x)-\ operatorname{ li}( x){\ frac{ 1}{ 8\pi}}{\ sqrt{ x}}\ log( x),\ qquad{\ text{ for all}} x\ geq 2657,} where π( x) is the prime-counting function, and log( x) is the natural logarithm of x.

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