Analytic Number Theory¶

8 domain-specific abstractions whose origin domain is Analytic Number Theory.

Brun sieve — A combinatorial sieve that estimates integers avoiding specified prime divisibility conditions by truncating inclusion-exclusion with alternating upper and lower bounds.
Dirichlet density — An analytic density of a set of primes defined by its weighted prime Dirichlet series as the exponent approaches one from above.
Dirichlet series — A complex series whose nth term is a coefficient multiplied by n raised to a complex negative exponent, serving as a multiplicative generating function in analytic number theory.
Hurwitz zeta function — A two-parameter zeta function formed by summing inverse powers of an arithmetic progression and extended meromorphically beyond its defining half-plane.
Lambert series — A generating series of the form sum a_n q^n divided by one minus q^n, whose expanded coefficients are divisor sums of the original sequence.
Mertens function — The summatory function of the Möbius function, equal to the running difference between square-free integers with even and odd numbers of prime factors.
Niven's constant — The limiting average, over positive integers, of the largest exponent in each integer’s prime factorization.
Prime-counting function — The arithmetic function pi of x that counts prime numbers less than or equal to a real bound x.