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[Texts]## 11N: Multiplicative number theory |

- 11N05: Distribution of primes
- 11N13: Primes in progressions [See also 11B25]
- 11N25: Distribution of integers with specified multiplicative constraints
- 11N30: Turán theory [See also 30Bxx]
- 11N32: Primes represented by polynomials; other multiplicative structure of polynomial values
- 11N35: Sieves
- 11N36: Applications of sieve methods
- 11N37: Asymptotic results on arithmetic functions
- 11N45: Asymptotic results on counting functions for algebraic and topological structures
- 11N56: Rate of growth of arithmetic functions
- 11N60: Distribution functions associated with additive and positive multiplicative functions
- 11N64: Other results on the distribution of values or the characterization of arithmetic functions
- 11N69: Distribution of integers in special residue classes
- 11N75: Applications of automorphic functions and forms to multiplicative problems [See also 11Fxx]
- 11N80: Generalized primes and integers
- 11N99: None of the above, but in this section

Parent field: 11: Number Theory

Browse all (old) classifications for this area at the AMS.

- Davenport, Harold: "Multiplicative number theory", Graduate Texts in Mathematics, 74. Springer-Verlag, New York-Berlin, 1980. 177 pp. ISBN 0-387-90533-2
- Huxley, M. N. "Dirichlet polynomials", in Elementary and analytic theory of numbers (Warsaw, 1982), 307--316, Banach Center Publ., 17, PWN, Warsaw, 1985.
- Elliott, P. D. T. A.: "Arithmetic functions and integer products", Grundlehren der Mathematischen Wissenschaften 272, Springer-Verlag, New York-Berlin, 1985. 461 pp. ISBN 0-387-96094-5

- Bonse's inequality; each prime no more than sqrt(prod(previous))
- Proof of Bertrand's postulate: there is always a prime between n and 2n.
- Bertrand's postulate: there is a prime between n and 2n
- Best proven estimates on the distribution of primes.
- Upper bounds for the n-th prime number
- Is there always a prime in the range...
- How far apart are the primes?
- Estimates of gaps between consecutive primes
- Estimates for the distance from one prime number to the next
- Tables, algorithms, citations on pi(N), the the number of primes up to N
- Table: number of primes less than 2^N, N=1, 2, ..., 32
- "Prime server": ask it for the 20 000 000-th prime
- When does the number of primes less than x first exceed Li(x)? (Skewes' number)
- Large departures of pi(x) from Li(x)
- Review of selected literature on twin primes
- Numerical data for the Twin-Prime conjecture.
- Brun's constant (sum of reciprocals of all twin primes
- Brun's constant counting twin primes.
- Probabilistic conjectures regarding sequences with infinitely many primes
- Generalization of Goldbach, Twin Prime conjectures (distributions of primes)
- Maximum number of primes in intervals (prime constellations)
- Why we expect infinitely many primes of the form (10^n-7)/3 (prime for all n < 9 )
- Classic estimate of the sum of logs of first few primes.
- Sum of ln ln p for all primes less than P
- Least common multiple of the first n integers, about exp(n)
- Estimates of the product of the first N primes.
- Find integers N divisible by all primes up to sqrt(N)
- The n-th prime is roughly e times the geometric mean of the ones before it.
- Sum of log(log(p)) over primes less than N
- Estimating sum f(p) over primes p (e.g. f(x)=1/x )
- Mertens' Conjecture: is sum_{n < x} µ(n) always less than sqrt(x)? (no)
- Estimates of theta(x)=sum( log(p), p < x) and the relation to the prime number theorem.
- Evaluate sum of 1/(phi(n)sigma(n))
- Incompatibility of two "certain" conjectures (prime constellations vs pi(x+y) < pi(x)+pi(y).)
- Citations for references on smooth numbers
- Polynomials taking prime values; Friedlander and Iwaniec theorem
- How much did Dirichlet prove about primes in progressions?
- Fine points of distribution of primes in arithmetic progression
- Infinitude of primes in the congruence classes mod 8
- Primes in arithmetic progressions mod 11, and approximations of pi
- Minimal values for sum of prime divisors function
- Maximal values for number of divisors function
- Minimal values for Euler's phi function
- Sum of values of Euler-phi(n), n through N
- Mertens' Conjecture
- Finding sets of integers in short intervals, whose product is a square
- Carmichael numbers: Korselt's criterion
- Long arithmetic progressions consisting only of (consecutive) primes

Last modified 2000/01/14 by Dave Rusin. Mail: