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- Brun–Titchmarsh_theorem abstract "In analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of prime numbers in arithmetic progression. It states that, if counts the number of primes p congruent to a modulo q with p ≤ x, thenfor all q < x. The result was proven by sieve methods by Montgomery and Vaughan; an earlier result of Brun and Titchmarsh obtained a weaker version of this inequality with an additional multiplicative factor of .If "q" is relatively small, e.g., , then there exists a better bound:This is due to Y. Motohashi (1973). He used a bilinear structure in the error term in the Selberg sieve, discovered by himself. Later this idea of exploiting structures in sieving errors developed into a major method in Analytic Number Theory, due to H. Iwaniec's extension to combinatorial sieve.By contrast, Dirichlet's theorem on arithmetic progressions gives an asymptotic result, which may be expressed in the formbut this can only be proved to hold for the more restricted range q < (log x)c for constant c: this is the Siegel–Walfisz theorem.".
- Brun–Titchmarsh_theorem wikiPageID "18253221".
- Brun–Titchmarsh_theorem wikiPageRevisionID "577628647".
- Brun–Titchmarsh_theorem first "H.".
- Brun–Titchmarsh_theorem id "b/b110970".
- Brun–Titchmarsh_theorem last "Mikawa".
- Brun–Titchmarsh_theorem subject Category:Theorems_about_prime_numbers.
- Brun–Titchmarsh_theorem subject Category:Theorems_in_analytic_number_theory.
- Brun–Titchmarsh_theorem comment "In analytic number theory, the Brun–Titchmarsh theorem, named after Viggo Brun and Edward Charles Titchmarsh, is an upper bound on the distribution of prime numbers in arithmetic progression. It states that, if counts the number of primes p congruent to a modulo q with p ≤ x, thenfor all q < x.".
- Brun–Titchmarsh_theorem label "Brun–Titchmarsh theorem".
- Brun–Titchmarsh_theorem label "Teorema de Brun–Titchmarsh".
- Brun–Titchmarsh_theorem label "مبرهنة برون-تيتشمارش".
- Brun–Titchmarsh_theorem sameAs Brun%E2%80%93Titchmarsh_theorem.
- Brun–Titchmarsh_theorem sameAs Teorema_de_Brun–Titchmarsh.
- Brun–Titchmarsh_theorem sameAs Q4979609.
- Brun–Titchmarsh_theorem sameAs Q4979609.
- Brun–Titchmarsh_theorem wasDerivedFrom Brun–Titchmarsh_theorem?oldid=577628647.