La hipótesis de Riemann: formulación desde el análisis matemático y su relación con los números primos

Abstract

This work studies the theoretical foundations that allow for the formulation of the Riemann hypothesis, starting from key results in complex analysis. It begins with a brief historical context about the origin of the problem and its importance in number theory. Then, using the principles of complex analysis, the Gamma function is constructed, along with some of its most important properties such as Stirling's formula and the calculation of its residues. With this, the Riemann zeta function is defined, its representation through Euler's product, and the functional equation, which allows the zeta function to be extended to values with negative real parts. Finally, we state the Riemann hypothesis and its connection with the distribution of prime numbers.