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Linnik's Theorem
Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive ''c'' and ''L'' such that, if we denote p(''a'',''d'') the least prime in the arithmetic progression :a + nd,\ where ''n'' runs through the positive integers and ''a'' and ''d'' are any given positive coprime integers with 1 ≤ ''a'' ≤ ''d'' − 1, then: : \operatorname(a,d) < c d^. \; The theorem is named after Yuri Vladimirovich Linnik, who proved it in 1944. Although Linnik's proof showed ''c'' and ''L'' to be effectively computable, he provided no numerical va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Number Theory
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 1837 introduction of Dirichlet ''L''-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the Prime Number Theorem and Riemann zeta function) and additive number theory (such as the Goldbach conjecture and Waring's problem). Branches of analytic number theory 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 numb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The American Mathematical Society
The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abstracted and indexed in: 2011. American Mathematical Society. * Mathematical Reviews * Zentralblatt MATH * Science Citation Index * ISI Alerting Services * CompuMath Citation Index * [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proc
Proc may refer to: * Proč, a village in eastern Slovakia * '' Proč?'', a 1987 Czech film * procfs or proc filesystem, a special file system (typically mounted to ) in Unix-like operating systems for accessing process information * Protein C (PROC) * Proc, a term in video game terminology * Procedures or process, in the programming language ALGOL 68 * People's Republic of China, the formal name of China * the official acronym for the Canadian House of Commons Standing Committee on Procedure and House Affairs * People's Republic of the Congo The People's Republic of the Congo () was a Marxist–Leninist socialist state that existed in the Republic of the Congo from 1969 to 1992. The People's Republic of the Congo was founded in December 1969 as the first Marxist-Leninist state ... * Pro*C, a programming language {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger Heath-Brown
David Rodney "Roger" Heath-Brown is a British mathematician working in the field of analytic number theory. Education He was an undergraduate and graduate student of Trinity College, Cambridge; his research supervisor was Alan Baker. Career and research In 1979 he moved to the University of Oxford, where from 1999 he held a professorship in pure mathematics. He retired in 2016. Heath-Brown is known for many striking results. He proved that there are infinitely many prime numbers of the form ''x''3 + 2''y''3. In collaboration with S. J. Patterson in 1978 he proved the Kummer conjecture on cubic Gauss sums in its equidistribution form. He has applied Burgess's method on character sums to the ranks of elliptic curves in families. He proved that every non-singular cubic form over the rational numbers in at least ten variables represents 0. Heath-Brown also showed that Linnik's constant is less than or equal to 5.5. More recently, Heath-Brown is known for his pi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liu Jian Min
Liu (; or ) is an East Asian surname. pinyin: in Mandarin Chinese, in Cantonese. It is the family name of the Han dynasty emperors. The character originally meant 'battle axe', but is now used only as a surname. It is listed 252nd in the classic text Hundred Family Surnames. Today, it is the 4th most common surname in mainland China as well as one of the most common surnames in the world. Distribution In 2019 劉 was the fourth most common surname in mainland China. Additionally, it was the most common surname in Jiangxi province. In 2013 it was found to be the 5th most common surname, shared by 67,700,000 people or 5.1% of the population, with the province with the most people being Shandong.中国四百大姓, 袁义达, 邱家儒, Beijing Book Co. Inc., 1 January 2013 Origin One source is that they descend from the Qí (祁) clan of Emperor Yao. For example, the founding emperor of the Han dynasty (one of China's golden ages), Liu Bang (Emperor Gaozu of Han) was a descend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acta Arith
''Acta Arithmetica'' is a scientific journal of mathematics publishing papers on number theory. It was established in 1935 by Salomon Lubelski and Arnold Walfisz. The journal is published by the Institute of Mathematics of the Polish Academy of Sciences. References External links Online archives (Library of Science, Issues: 1935–2000) 1935 establishments in Poland Number theory journals Academic journals established in 1935 Polish Academy of Sciences academic journals Biweekly journals Academic journals associated with learned and professional societies {{math-journal-stub English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
