Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Analytic_number_theory> ?p ?o. }
Showing items 1 to 35 of
35
with 100 items per page.
- Analytic_number_theory abstract "In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. Another major milestone in the subject is the prime number theorem.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. Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions. 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.Developments within analytic number theory are often refinements of earlier techniques, which reduce the error terms and widen their applicability. For example, the circle method of Hardy and Littlewood was conceived as applying to power series near the unit circle in the complex plane; it is now thought of in terms of finite exponential sums (that is, on the unit circle, but with the power series truncated). The needs of diophantine approximation are for auxiliary functions that are not generating functions—their coefficients are constructed by use of a pigeonhole principle—and involve several complex variables.The fields of diophantine approximation and transcendence theory have expanded, to the point that the techniques have been applied to the Mordell conjecture.The biggest technical change after 1950 has been the development of sieve methods, particularly in multiplicative problems. These are combinatorial in nature, and quite varied. The extremal branch of combinatorial theory has in return been greatly influenced by the value placed in analytic number theory on quantitative upper and lower bounds. Another recent development is probabilistic number theory, which uses methods from probability theory to estimate the distribution of number theoretic functions, such as how many prime divisors a number has.".
- Analytic_number_theory thumbnail Complex_zeta.jpg?width=300.
- Analytic_number_theory wikiPageID "251513".
- Analytic_number_theory wikiPageRevisionID "605427389".
- Analytic_number_theory align "right".
- Analytic_number_theory hasPhotoCollection Analytic_number_theory.
- Analytic_number_theory quote """".
- Analytic_number_theory quote ""…it is very probable that all roots are real. Of course one would wish for a rigorous proof here; I have for the time being, after some fleeting vain attempts, provisionally put aside the search for this, as it appears dispensable for the next objective of my investigation."".
- Analytic_number_theory source "Riemann's statement of the Riemann hypothesis, from his 1859 paper.".
- Analytic_number_theory width "30.0".
- Analytic_number_theory subject Category:Analytic_number_theory.
- Analytic_number_theory comment "In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions.".
- Analytic_number_theory label "Analytic number theory".
- Analytic_number_theory label "Analytische Zahlentheorie".
- Analytic_number_theory label "Analytische getaltheorie".
- Analytic_number_theory label "Teoria analitica dei numeri".
- Analytic_number_theory label "Teoria analítica dos números".
- Analytic_number_theory label "Teoría analítica de números".
- Analytic_number_theory label "Théorie analytique des nombres".
- Analytic_number_theory label "Аналитическая теория чисел".
- Analytic_number_theory label "نظرية الأعداد التحليلية".
- Analytic_number_theory label "解析数论".
- Analytic_number_theory sameAs Analytische_Zahlentheorie.
- Analytic_number_theory sameAs Teoría_analítica_de_números.
- Analytic_number_theory sameAs Théorie_analytique_des_nombres.
- Analytic_number_theory sameAs Teoria_analitica_dei_numeri.
- Analytic_number_theory sameAs 해석적_수론.
- Analytic_number_theory sameAs Analytische_getaltheorie.
- Analytic_number_theory sameAs Teoria_analítica_dos_números.
- Analytic_number_theory sameAs m.01lbbc.
- Analytic_number_theory sameAs Q10843274.
- Analytic_number_theory sameAs Q10843274.
- Analytic_number_theory wasDerivedFrom Analytic_number_theory?oldid=605427389.
- Analytic_number_theory depiction Complex_zeta.jpg.
- Analytic_number_theory isPrimaryTopicOf Analytic_number_theory.