The Generalized Riemann Hypothesis

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Building on the foundations laid by Bernhard Riemann in the 19th century, the Generalized Riemann Hypothesis (GRH) extends the famous conjecture about the distribution of prime numbers and their connection to the zeros of the Riemann Zeta Function.

The Generalizations of the Riemann Hypothesis regard a class of functions known as Global L-functions rather than a single one.
One can apply similar conditions to these functions and ask if the nontrivial zeros again occur only when Re(s)=1/2

In particular, the Generalized Riemann Hypothesis focuses on Dirichlet L-functions.

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