Tell me what is Riemann hypothesis.
Answers
Answer:
Riemann hypothesis, in number theory, hypothesis by German mathematician Bernhard Riemann concerning the location of solutions to the Riemann zeta function, which is connected to the prime number theorem and has important implications for the distribution of prime numbers. Riemann included the hypothesis in a paper, “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” (“On the Number of Prime Numbers Less Than a Given Quantity”), published in the November 1859 edition of Monatsberichte der Berliner Akademie (“Monthly Review of the Berlin Academy”).
Step-by-step explanation:
The zeta function is defined as the infinite series
ζ(s) = 1 + 2−s + 3−s + 4−s + ⋯,
or, in more compact notation,
formula for the zeta function, Riemann hypothesis,
where the summation (Σ) of terms for n runs from 1 to infinity through the positive integers and s is a fixed positive integer greater than 1. The zeta function was first studied by Swiss mathematician Leonhard Euler in the 18th century. (For this reason, it is sometimes called the Euler zeta function. For ζ(1), this series is simply the harmonic series, known since antiquity to increase without bound—i.e., its sum is infinite.) Euler achieved instant fame when he proved in 1735 that ζ(2) = π2/6, a problem that had eluded the greatest mathematicians of the era, including the Swiss Bernoulli family (Jakob, Johann, and Daniel). More generally, Euler discovered (1739) a relation between the value of the zeta function for even integers and the Bernoulli numbers, which are the coefficients in the Taylor series expansion of x/(ex − 1). (See also exponential function.) Still more amazing, in 1737 Euler discovered a formula relating the zeta function, which involves summing an infinite sequence of terms containing the positive integers, and an infinite product that involves every prime number:
Answer: ITS TOO TOUGH
Step-by-step explanation: