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Euler solved the so-called Basel problem in his twenties by evaluating sums like \(\sum _{n=1}^\infty \frac{1}{n^2}\) in the mid 1730 s, but it was Riemann who saw the importance of studying the sums \(\sum _{n=1}^\infty \frac{1}{n^s}\) as a function \(\zeta (s)\) of the complex variable s. In his pioneering 1859 article [Rie59], Riemann brought to light a powerful relationship between the zeros of the zeta function and the distribution of prime numbers.

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Classical Zeta Functions and L-Functions

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  • 发表日期：

    2025年

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  • Claus Sorensen

摘要

Euler solved the so-called Basel problem in his twenties by evaluating sums like \(\sum _{n=1}^\infty \frac{1}{n^2}\) in the mid 1730 s, but it was Riemann who saw the importance of studying the sums \(\sum _{n=1}^\infty \frac{1}{n^s}\) as a function \(\zeta (s)\) of the complex variable s. In his pioneering 1859 article [Rie59], Riemann brought to light a powerful relationship between the zeros of the zeta function and the distribution of prime numbers.