Riemann Hypothesis/Preliminary knowledge

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Glossary[edit | edit source]

Convergence of a series:

Take some complex-valued sequence, , and let,

The sequence may be referred to as convergent if tends towards some finite limit, as becomes infinitely large. Specifically, the difference between and becomes arbitrarily small as becomes arbitrarily large, ie.


Dirichlet series:

A Dirichlet series is an infinite series of the form,

Where and are complex numbers, and is some strictly increasing sequence of nonnegative real numbers. Within this book we look at a special case. That is the case of , a Dirichlet L-series,

Gamma function:

The Gamma function extends the factorial to all complex numbers bar non-positive integers. It is defined by the improper integral,

Satisfying the properties,