Editing Analytic number theory (section)

==Branches of analytic number theory==
Analytic number theory can be split up into two major parts, divided more by the type of problems they attempt to solve than fundamental differences in technique.<ref>{{Cite web |last=Hildebrand |first=A.J. |year=2005 |title=Introduction to Analytic Number Theory Math 531 Lecture Notes, Fall 2005 |url=https://faculty.math.illinois.edu/~hildebr/ant/main.pdf#page=21 }}</ref>
*[[Multiplicative number theory]] deals with the distribution of the [[prime number]]s, such as estimating the number of primes in an interval, and includes the prime number theorem and [[Dirichlet's theorem on arithmetic progressions|Dirichlet's theorem on primes in arithmetic progressions]].<ref>{{cite book
 |last = Davenport
 |first = Harold 
 |author-link = Harold Davenport
 |year = 2013
 |title = Multiplicative number theory
 |series = Graduate Texts in Mathematics 
 |volume = 74 
 |url = https://books.google.com/books?id=SFztBwAAQBAJ&pg=PA1
 |publisher = Springer-Verlag
 |page = 1
 |isbn = 978-1-4757-5929-7
 |doi = 10.1007/978-1-4757-5927-3
}}</ref>
*[[Additive number theory]] is concerned with the additive structure of the integers, such as [[Goldbach's conjecture]] that every even number greater than 2 is the sum of two primes. One of the main results in additive number theory is the solution to [[Waring's problem]].<ref>{{cite book
 |last = Nathason
 |first =  Melvyn B.
 |author-link = Melvyn B. Nathanson
 |year = 2013
 |title = Additive Number Theory, The Classical Bases
 |url = https://books.google.com/books?id=nbjVBwAAQBAJ
 |publisher = Springer-Verlag
 |page = vii&ndash;viii
 |isbn = 978-0-387-94656-6
}}</ref>