What is an $L$-function?

The Riemann Hypothesis is an assertion about the zeros of the Riemann $\zeta$-function. Generalizations of the $\zeta$-function have been discovered, for which the analogue of the Riemann Hypothesis is also conjectured.

These generalizations of the $\zeta$-function are known as ``zeta-functions'' or ``$L$-functions.'' In this section we describe attempts to determine the collection of functions that deserve to be called L-functions.

Back to the main index for The Riemann Hypothesis.