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WindowTitle->21. The Riemann Zeta Function | Introduction to Number Theory
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In this lesson, we will not dig deep into analytic number theory. We will \
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 ", in his 1859 article, generalized Euler\[CloseCurlyQuote]s definition for \
complex variables. Most importantly, he demonstrated a relationship between \
the function\[CloseCurlyQuote]s zeros and the distribution of prime numbers. \
To this day, that article is considered to be one of the most important in \
number theory."
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Cell["Plots of the Riemann Zeta Function", "Subsection",
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One simply cannot resist the temptation of plotting a function.\
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Cell["\<\
Here is the plot of the Riemann zeta function as a function of a real \
variable: \
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Surprisingly enough, the Riemann zeta function is related to the distribution \
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Euler made the first connection between zeta functions and prime numbers when \
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This remarkable connection established the basis of modern prime number \
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If the Riemann hypothesis turns out to be true, then it will shed light on \
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