La Funció ζ de Riemann

Authors

  • Jordi Quer

Abstract

In November 1859 Riemann sent a six pages manuscript to the Berlin Academy entitled «On the number of primes less than a given magnitude», which is his the only publication devoted to Number Theory in all of his scientific production. This work, one of the masterpieces in the whole history of mathematics, pioneered the application of analytic techniques in the study of arithmetic problems. In this work Riemann introduces his well-known \theta-function and provides several of its properties from which he derives results on the accumulation of prime numbers. He also states the famous conjecture on the zeroes of the \theta function which has become known as the Riemann Hypothesis. After resisting the attempts of many of the best mathematicians, the Riemann Hypothesis is considered one of the most important open problems in mathematics nowadays.
The purpose of these notes is to explain the contents of this work and the fundamental role it has played in the study of the distribution of the prime numbers.

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Published

2008-02-28

How to Cite

Quer, J. (2008). La Funció ζ de Riemann. Butlletí De La Societat Catalana De Matemàtiques, 22(2), 197–228. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/33989.001

Issue

Vol. 22 No. 2 (2007)

Section

Articles

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