Примери за използване на Zeta function на Английски и техните преводи на Български
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Gram also worked on the Riemann zeta function.
The zeta function satisfies the functional equation.
Where ζ(s, k) is the Hurwitz zeta function.
The Euler zeta function is defined for real numbers greater than 1.
Other series related to the zeta function include.
As it stands the Euler zeta function S(x) is defined for real numbers x that are greater than 1.
Which coincides with the Riemann zeta function when z= 1.
There are a number of related zeta functions that can be considered to be generalizations of the Riemann zeta function.
Selberg's trace formula,Selberg's zeta function,….
On the number of zeros of the Riemann zeta function on short intervals of the critical line.
His work was in number theory,in particular the zeta function.
It states that the nontrivial zeros of the zeta function all have a real part equal to 1/2.
The following are the most commonly used values of the Riemann zeta function.
Distribution of zeros of the Riemann zeta function on the short intervals of the critical line.
The real part of every non-trivial zero of the Riemann zeta function is 1/2.".
In the theory of the Riemann zeta function, the set{s∈ ℂ: Re(s)= 1/2} is called the critical line.
The darker horizontal bands are the shadows of zeros of the Riemann zeta function.
In 1737 he proved the connection of the zeta function with the series of prime numbers.
The third of his conjectures was a generalisation of the Riemann hypothesis on the zeta function.
First, the analogue of the Riemann conjecture for the zeta function of a curve over finite fields.
Many more papers on formal groups followed,in particular relating them to the zeta function.
He also published papers on the gamma function, the zeta function and partial differential equations.
Some of this important work on the zeta function was due to Bohr alone, some came from the collaboration with Landau.
Γ can also be expressed as an infinite sum whose terms involve the Riemann zeta function evaluated at positive integers.
Lower bounds for the maximum modulus of zeta function in small domains of the critical strip and in short intervals of the critical line.
Riemann considered a very different question to the one Euler had considered,for he looked at the zeta function as a complex function rather than a real one.
In the paper he stated that the zeta function had infinitely many nontrivial roots and that it seemed probable that they all have real part 1/2.
Bohr and Landau proved that all butan infinitesimal proportion of the zeros of the zeta function lie in a small neighbourhood of the line s= 1/2.
In 1737 he proved the connection of the zeta function with the series of prime numbers giving the famous relation.
Other than the prime number theorem,Vallée Poussin's only contributions to prime numbers were contained in two papers on the Riemann zeta function which he published in 1916.