Definition:Analytic Number Theory

Definition

Analytic number theory is a branch of number theory which uses tools from analysis to solve problems about the integers.

Also see

• Results about analytic number theory can be found here.

Historical Note

The field of analytic number theory was effectively created by Leonhard Paul Euler in $1737$, on the occasion of his discovery of two results:

Sum of Reciprocals of Powers as Euler Product

and:

Sum of Reciprocals of Primes is Divergent.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.16$: The Sequence of Primes