Analytic number theory | Wikipedia audio article
Channel: wikipedia tts
Date: 2018-12-27

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Analytic_number_theory


00:00:41 1 Branches of analytic number theory
00:01:41 2 History
00:01:50 2.1 Precursors
00:03:38 2.2 Dirichlet
00:05:10 2.3 Chebyshev
00:06:15 2.4 Riemann
00:07:38 2.5 Hadamard and de la Vallée-Poussin
00:08:17 2.6 Modern times
00:08:57 3 Problems and results
00:09:03 3.1 Multiplicative number theory
00:10:55 3.2 Additive number theory
00:11:29 3.3 Diophantine problems
00:17:11 4 Methods of analytic number theory
00:19:05 4.1 Dirichlet series
00:23:40 4.2 Riemann zeta function
00:23:52 5 See also
00:27:34 6 Notes
00:29:00 7 References
00:32:10 8 Further reading



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SUMMARY
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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-functions 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).