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Analytic number theory
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, analytic number theory is a branch of <a href="/facts/Number_theory/zhoa7zrc">number theory</a> that uses methods from <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a> to solve problems about the <a href="/facts/Integer/PUwwrawx">integers</a>. It is often said to have begun with <a href="/facts/Peter_Gustav_Lejeune_Dirichlet/b5UIU7Uy">Peter Gustav Lejeune Dirichlet</a>'s 1837 introduction of <a href="/facts/Dirichlet_L-function/my8hc6Qy">Dirichlet <i>L</i>-functions</a> to give the first proof of <a href="/facts/Dirichlet%2527s_theorem_on_arithmetic_progressions/yFyJaE2d">Dirichlet's theorem on arithmetic progressions</a>. It is well known for its results on <a href="/facts/Prime_numbers/L20FLkgn">prime numbers</a> (involving the <a href="/facts/Prime_Number_Theorem/3KA9egls">Prime Number Theorem</a> and <a href="/facts/Riemann_zeta_function/MnfRu7lY">Riemann zeta function</a>) and <a href="/facts/Additive_number_theory/43Fm5NFN">additive number theory</a> (such as the <a href="/facts/Goldbach_conjecture/967UhtUU">Goldbach conjecture</a> and <a href="/facts/Waring%2527s_problem/Qq5My8wy">Waring's problem</a>). </p>