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Analytic number theory
In
mathematics
,
analytic number theory
is a branch of
number theory
that uses methods from
mathematical analysis
to solve problems about the integers. It is often said to have begun with
Peter Gustav Lejeune Dirichlet
's 1837 introduction of
Dirichlet L-function
s to give the first proof of
Dirichlet's theorem on arithmetic progressions
. It is well known for its results on
prime numbers
(involving the
Prime Number Theorem
and
Riemann zeta function
) and
additive number theory
(such as the
Goldbach conjecture
and
Waring's problem
).
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