In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part ⁠ 1 / 2 ⁠. Many consider it to be the most important unsolved problem in pure mathematics. [1]

Mar 2, 2025 · 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 …

Jul 1, 2024 · The Riemann hypothesis concerns the basic building blocks of natural numbers: prime numbers, values greater than 1 that are only divisible by 1 and themselves. Examples include...

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial Riemann zeta function zeros, i.e., the values of s other than -2, -4, -6, ... such that zeta(s)=0 (where zeta(s) is the Riemann zeta function) all lie on the "critical line" sigma=R[s ...

The Riemann hypothesis asks a question about a special thing called the Riemann zeta function. If the answer to the question is "yes", this would mean mathematicians can know more about prime numbers .

The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann’s 1859 paper, it asserts that all the ‘non-obvious’ zeros of the zeta function are complex numbers with real part 1/2.

Our aim is to give an introduction to the Riemann Hypothesis and a panoramic view of the world of zeta and L-functions. We rst review Riemann's foundational article and discuss the mathematical background of the time and his possible motivations for …

Jun 25, 2024 · The Riemann Hypothesis was formulated by Bernhard Riemann in 1859 and remains one of the most important unsolved problems in mathematics. Mathematicians have made numerous attempts to prove the Riemann Hypothesis, but it has eluded solution, earning it the title of “the greatest puzzle in math.”

Jun 24, 2013 · This hypothesis, made by German mathematician Bernhard Riemann in 1859 is still unsolved over 150 years later – despite some of the greatest mathematical minds of the 2oth century attempting the problem.

The Riemann hypothesis is the conjecture made by Riemann that the Euler zeta func- tion has no zeros in a half–plane larger than the half–plane which has no zeros by the convergence of the Euler product.