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Tomio Kubota
(6 December 1930 – 30 June 2020) was a Japanese mathematician working in number theory. His contributions include works on p-adic L functions and real-analytic automorphic forms. His work on p-adic L-functions, later recognised as an aspect of Iwasawa theory, was done jointly with Leopoldt. He extended the concept of metaplectic group, in a way significant for arithmetic applications. This opened a field for later research on associated Dirichlet series and automorphic forms, and was a major step in the solution of Kummer's conjecture.Jeff Hoffstein, ''Eisenstein Series and Theta Functions on the Metaplectic Group'', pp. 73-78, in Maruti Ram Murty, ''Theta Functions: From the Classical to the Modern'' (1993). Works *''On automorphic functions and the reciprocity law in a number field''. Kinokuniya, Tokyo 1969 *''Notes on analytic theory of numbers''. University of Chicago Press The University of Chicago Press is the largest and one of the oldest university presses in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaplectic Group
In mathematics, the metaplectic group Mp2''n'' is a double cover of the symplectic group Sp2''n''. It can be defined over either real or ''p''-adic numbers. The construction covers more generally the case of an arbitrary local or finite field, and even the adele ring, ring of adeles. The metaplectic group has a particularly significant infinite-dimensional linear representation, the Weil representation. It was used by André Weil to give a representation-theoretic interpretation of theta functions, and is important in the theory of modular forms of half-integral weight and the theta correspondence. Definition The fundamental group of the symplectic group, symplectic Lie group Sp2n(R) is infinite cyclic group, infinite cyclic, so it has a unique connected double cover, which is denoted Mp2''n''(R) and called the metaplectic group. The metaplectic group Mp2(R) is ''not'' a matrix group: it has no faithful representation, faithful finite-dimensional representations. Therefore, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1930 Births
Year 193 ( CXCIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sosius and Ericius (or, less frequently, year 946 '' Ab urbe condita''). The denomination 193 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * January 1 – Year of the Five Emperors: The Roman Senate chooses Publius Helvius Pertinax, against his will, to succeed the late Commodus as Emperor. Pertinax is forced to reorganize the handling of finances, which were wrecked under Commodus, to reestablish discipline in the Roman army, and to suspend the food programs established by Trajan, provoking the ire of the Praetorian Guard. * March 28 – Pertinax is assassinated by members of the Praetorian Guard, who storm the imperial palace. The Empire is auc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Japanese Mathematicians
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman emperor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigekatu Kuroda
was a Japanese mathematician who worked in number theory and mathematical logic. In 1942 he became a professor at the newly founded Nagoya Imperial University, where he stayed for over twenty years. He is responsible for much of the effort in setting up its Department of Mathematics. He was married to the renowned number theorist Teiji Takagi's daughter Yakeo. The couple had three sons, all of whom became mathematicians, including S.-Y. Kuroda, who was a professor of linguistics at University of California, San Diego. He published a text on Foundations of Number Theory with Tomio Kubota (6 December 1930 – 30 June 2020) was a Japanese mathematician working in number theory. His contributions include works on p-adic L functions and real-analytic automorphic forms. His work on p-adic L-functions, later recognised as an aspect ... in 1963. References External links Sigekatu Kuroda / Written by J J O'Connor and E F Robertson Last Update July 2011 / School of Mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Chicago Press
The University of Chicago Press is the largest and one of the oldest university presses in the United States. It is operated by the University of Chicago and publishes a wide variety of academic titles, including ''The Chicago Manual of Style'', numerous academic journals, and advanced monographs in the academic fields. One of its quasi-independent projects is the BiblioVault, a digital repository for scholarly books. The Press building is located just south of the Midway Plaisance on the University of Chicago campus. History The University of Chicago Press was founded in 1890, making it one of the oldest continuously operating university presses in the United States. Its first published book was Robert F. Harper's ''Assyrian and Babylonian Letters Belonging to the Kouyunjik Collections of the British Museum''. The book sold five copies during its first two years, but by 1900 the University of Chicago Press had published 127 books and pamphlets and 11 scholarly journals, inclu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinokuniya
is a Japanese bookstore chain operated by , founded in 1927, with its first store located in Shinjuku, Tokyo, Japan. Its name translates to "Bookstore of Kii Province". The company has its headquarters in Meguro, Tokyo. One of the company's goals has been to cater to the interests of not only local Japanese clients, but to a wider, more diverse clientele. This is why its international bookstores have focused on supplying a wide range of both Japanese and English books. History Kinokuniya was originally a lumber and charcoal dealer in Yotsuya; and after the 1923 Great Kantō earthquake, the business was moved westward to a new location in Shinjuku, where it was refashioned into a book store by former president Moichi Tanabe, opening with a staff of five in January 1927. He named it after Kii Province, given that his ancestor was a servant of the Kii-Tokugawa family; they are not related to the Edo Period merchant Kinokuniya Bunzaemon. On the second floor was an art galler ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kummer Sum
In mathematics, Kummer sum is the name given to certain cubic Gauss sums for a prime modulus ''p'', with ''p'' congruent to 1 modulo 3. They are named after Ernst Kummer, who made a conjecture about the statistical properties of their arguments, as complex numbers. These sums were known and used before Kummer, in the theory of cyclotomy. Definition A Kummer sum is therefore a finite sum :\sum \chi(r)e(r/p) = G(\chi) taken over ''r'' modulo ''p'', where χ is a Dirichlet character taking values in the cube roots of unity, and where ''e''(''x'') is the exponential function exp(2π''ix''). Given ''p'' of the required form, there are two such characters, together with the trivial character. The cubic exponential sum ''K''(''n'',''p'') defined by :K(n,p)=\sum_^p e(nx^3/p) is easily seen to be a linear combination of the Kummer sums. In fact it is 3''P'' where ''P'' is one of the Gaussian periods for the subgroup of index 3 in the residues mod ''p'', under multiplication, while t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirichlet Series
In mathematics, a Dirichlet series is any series of the form \sum_^\infty \frac, where ''s'' is complex, and a_n is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Peter Gustav Lejeune Dirichlet. Combinatorial importance Dirichlet series can be used as generating series for counting weighted sets of objects with respect to a weight which is combined multiplicatively when taking Cartesian products. Suppose that ''A'' is a set with a function ''w'': ''A'' → N assigning a weight to each of the elements of ''A'', and suppose additionally that the fibre over any natural number under that weight is a finite set. (We call such an arrangement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinrich-Wolfgang Leopoldt
Heinrich-Wolfgang Leopoldt (22 August 1927 – 28 July 2011) was a German mathematician who worked on algebraic number theory. Leopoldt earned his Ph.D. in 1954 at the University of Hamburg under Helmut Hasse with the thesis ''Über Einheitengruppe und Klassenzahl reeller algebraischer Zahlkörper'' (''On group of unity and class number of real algebraic number fields''). As a postdoc, he was from 1956 to 1958 at the Institute for Advanced Study. In 1959, he obtained his habilitation degree at the University of Erlangen and was then at the University of Tübingen. From 1964, he was ordentlicher Professor at the University of Karlsruhe, where he was also Director of the Mathematics Institute. Leopoldt and Tomio Kubota introduced and investigated p-adic L-functions (now named after them). These functions are a component of Iwasawa theory and are a p-adic version of the Dirichlet L-functions. With Hans Zassenhaus he also worked on computer algebra and its applications in number t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
