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Ivan Matveevich Vinogradov
Ivan Matveevich Vinogradov ( rus, Ива́н Матве́евич Виногра́дов, p=ɪˈvan mɐtˈvʲejɪvʲɪtɕ vʲɪnɐˈɡradəf, a=Ru-Ivan_Matveyevich_Vinogradov.ogg; 14 September 1891 – 20 March 1983) was a Soviet mathematician, who was one of the creators of modern analytic number theory, and also a dominant figure in mathematics in the USSR. He was born in the Velikiye Luki district, Pskov Oblast. He graduated from the University of St. Petersburg, where in 1920 he became a Professor. From 1934 he was a Director of the Steklov Institute of Mathematics, a position he held for the rest of his life, except for the five-year period (1941–1946) when the institute was directed by Academician Sergei Sobolev. In 1941 he was awarded the Stalin Prize. In 1951 he became a foreign member of the Polish Academy of Sciences and Letters in Kraków. Mathematical contributions In analytic number theory, ''Vinogradov's method'' refers to his main problem-solving technique, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexandre Mikhailovich Vinogradov
Alexandre Mikhailovich Vinogradov (russian: Александр Михайлович Виноградов; 18 February 1938 – 20 September 2019) was a Russian and Italian mathematician. He made important contributions to the areas of differential calculus over commutative algebras, the algebraic theory of differential operators, homological algebra, differential geometry and algebraic topology, mechanics and mathematical physics, the geometrical theory of nonlinear partial differential equations and secondary calculus. Biography A.M. Vinogradov was born on 18 February 1938 in Novorossiysk. His father, Mikhail Ivanovich Vinogradov, was a hydraulics scientist; his mother, Ilza Alexandrovna Firer, was a medical doctor. Among his more distant ancestors, his great-grandfather, Anton Smagin, was a self-taught peasant and a deputy of the State Duma of the second convocation. Between 1955 and 1960 Vinogradov studied at the Mechanics and Mathematics Department of Moscow State Univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Sieve Method
The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein only a few residue classes are removed. The method has been further heightened by the larger sieve which removes arbitrarily many residue classes. Name Its name comes from its original application: given a set S \subset \ such that the elements of ''S'' are forbidden to lie in a set ''Ap'' ⊂ Z/''p'' Z modulo every prime ''p'', how large can ''S'' be? Here ''A''''p'' is thought of as being large, i.e., at least as large as a constant times ''p''; if this is not the case, we speak of a ''small sieve''. History The early history of the large sieve traces back to work of Yu. B. Linnik, in 1941, working on the problem of the least quadratic non-residue. Subsequently Alfréd Rényi worked on it, using probability methods. It was only two de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Zeta Function
The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s) = \sum_^\infty \frac = \frac + \frac + \frac + \cdots for \operatorname(s) > 1 and its analytic continuation elsewhere. The Riemann zeta function plays a pivotal role in analytic number theory, and has applications in physics, probability theory, and applied statistics. Leonhard Euler first introduced and studied the function over the reals in the first half of the eighteenth century. Bernhard Riemann's 1859 article "On the Number of Primes Less Than a Given Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation between its zeros and the distribution of prime numbers. This paper also contained the Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is consid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vinogradov's Theorem
In number theory, Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers. It is a weaker form of Goldbach's weak conjecture, which would imply the existence of such a representation for all odd integers greater than five. It is named after Ivan Matveyevich Vinogradov who proved it in the 1930s. Hardy and Littlewood had shown earlier that this result followed from the generalized Riemann hypothesis, and Vinogradov was able to remove this assumption. The full statement of Vinogradov's theorem gives asymptotic bounds on the number of representations of an odd integer as a sum of three primes. The notion of "sufficiently large" was ill-defined in Vinogradov's original work, but in 2002 it was shown that 101346 is sufficiently large. Additionally numbers up to 1020 had been checked via brute force methods, thus only a finite number of cases to check remained before the odd Goldbach conjecture would be proven or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Goldbach Problem
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that : Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.) This conjecture is called "weak" because if Goldbach's ''strong'' conjecture (concerning sums of two primes) is proven, then this would also be true. For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3). In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. As of 2018, the proof is widely accepted in the mathematics community, but it has not yet been published in a peer-reviewed journal. The proof was accepted for publication in the '' Annals of Mathematics Studies'' series in 2015, and has been undergoing further review and revision sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weyl Sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typical exponential sum may take the form :\sum_n e(x_n), summed over a finite sequence of real numbers ''x''''n''. Formulation If we allow some real coefficients ''a''''n'', to get the form :\sum_n a_n e(x_n) it is the same as allowing exponents that are complex numbers. Both forms are certainly useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in diophantine approximation. Estimates The main thrust of the subject is that a sum :S=\sum_n e(x_n) is ''trivially'' estimated by the number ''N'' of terms. That is, the absolute value :, S, \le N\, by the triangle inequality, since each summand has absolu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Sum
In mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function, usually expressed by means of the function :e(x) = \exp(2\pi ix).\, Therefore, a typical exponential sum may take the form :\sum_n e(x_n), summed over a finite sequence of real numbers ''x''''n''. Formulation If we allow some real coefficients ''a''''n'', to get the form :\sum_n a_n e(x_n) it is the same as allowing exponents that are complex numbers. Both forms are certainly useful in applications. A large part of twentieth century analytic number theory was devoted to finding good estimates for these sums, a trend started by basic work of Hermann Weyl in diophantine approximation. Estimates The main thrust of the subject is that a sum :S=\sum_n e(x_n) is ''trivially'' estimated by the number ''N'' of terms. That is, the absolute value :, S, \le N\, by the triangle inequality, since each summand has absolute va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
USSR State Prize
The USSR State Prize (russian: links=no, Государственная премия СССР, Gosudarstvennaya premiya SSSR) was the Soviet Union's state honor. It was established on 9 September 1966. After the dissolution of the Soviet Union, the prize was followed up by the State Prize of the Russian Federation. The State Stalin Prize ( Государственная Сталинская премия, ''Gosudarstvennaya Stalinskaya premiya''), usually called the Stalin Prize, existed from 1941 to 1954, although some sources give a termination date of 1952. It essentially played the same role; therefore upon the establishment of the USSR State Prize, the diplomas and badges of the recipients of Stalin Prize were changed to that of USSR State Prize. In 1944 and 1945, the last two years of the Second World War, the award ceremonies for the Stalin Prize were not held. Instead, in 1946 the ceremony was held twice: in January for the works created in 1943–1944 and in June for the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sergei Sobolev
Prof Sergei Lvovich Sobolev (russian: Серге́й Льво́вич Со́болев) HFRSE (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations. Sobolev introduced notions that are now fundamental for several areas of mathematics. Sobolev spaces can be defined by some growth conditions on the Fourier transform. They and their embedding theorems are an important subject in functional analysis. Generalized functions (later known as distributions) were first introduced by Sobolev in 1935 for weak solutions, and further developed by Laurent Schwartz. Sobolev abstracted the classical notion of differentiation, so expanding the range of application of the technique of Newton and Leibniz. The theory of distributions is considered now as the calculus of the modern epoch. Life He was born in St. Petersburg as the son of Lev Alexandrovich Sobolev, a lawyer, and his wife, Natalya Georgievna. His city ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steklov Institute Of Mathematics
Steklov Institute of Mathematics or Steklov Mathematical Institute (russian: Математический институт имени В.А.Стеклова) is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Steklov, who in 1919 founded the Institute of Physics and Mathematics in Leningrad. In 1934, this institute was split into separate parts for physics and mathematics, and the mathematical part became the Steklov Institute. At the same time, it was moved to Moscow. The first director of the Steklov Institute was Ivan Matveyevich Vinogradov. From 19611964, the institute's director was the notable mathematician Sergei Chernikov. The old building of the Institute in Leningrad became its Department in Leningrad. Today, that department has become a separate institute, called the ''St. Petersburg Department of Steklov Institute of Mathematics of Russian Academy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saint Petersburg State University
Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the Great, the university from the beginning has had a focus on fundamental research in science, engineering and humanities. During the Soviet period, it was known as Leningrad State University (russian: Ленинградский государственный университет). It was renamed after Andrei Zhdanov in 1948 and was officially called "Leningrad State University, named after A. A. Zhdanov and decorated with the Order of Lenin and the Order of the Red Banner of Labour." Zhdanov's was removed in 1989 and Leningrad in the name was officially replaced with Saint Petersburg in 1992. It is made up of 24 specialized faculties (departments) and institutes, the Academic Gymnasium, the Medical College, the College of Physical Culture ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
