Riemannféle

Riemannféle refers to a collection of mathematical concepts and problems that originated from or are related to the work of Bernhard Riemann. One of the most famous and significant of these is the Riemann hypothesis.

The Riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function. The zeta function, denoted by ζ(s), is a function of a complex variable s. The Riemann hypothesis states that all non-trivial zeros of the Riemann zeta function lie on the critical line, which is the line in the complex plane where the real part of s is equal to 1/2. This hypothesis has profound implications for number theory, particularly for the distribution of prime numbers.

Other concepts associated with Riemann's work include Riemannian geometry, which is a field of differential geometry that studies Riemannian manifolds. These are differentiable manifolds equipped with a Riemannian metric, which allows for the measurement of distances and angles. Riemannian geometry is fundamental to Einstein's theory of general relativity.

The term "Riemannféle" can also encompass various other contributions by Riemann, such as his work on Riemann surfaces, which are complex manifolds of one complex dimension, and his contributions to the theory of partial differential equations. The impact of Riemann's ideas on mathematics and physics is extensive and continues to be a subject of active research.