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Zwegers
Sander Pieter Zwegers (born April 16, 1975) is a Dutch mathematician who made a connection between Maass forms and Srinivasa Ramanujan's mock theta functions in 2002. He was born in Oosterhout. After a period at the Max-Planck Institute in Bonn, he became an assistant professor at the University College Dublin in 2008. Since 2011, he has been is professor of number theory at the University of Cologne. Research In 1976, the American mathematician George Andrews found what is nowadays known as the "Lost Notebook Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts were unknown to all but a few mathematicians until i ..." of Ramanujan. It contains many remarkable results, including the mysterious mock theta functions. This notebook contains what many specialists regard as Ramanujan’s deepest work. It was Sander Zwegers who, as a PdD stude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mock Theta Function
In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight . The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Sander Zwegers discovered that adding certain non-holomorphic functions to them turns them into harmonic weak Maass forms. History Ramanujan's 12 January 1920 letter to Hardy listed 17 examples of functions that he called mock theta functions, and his lost notebook contained several more examples. (Ramanujan used the term "theta function" for what today would be called a modular form.) Ramanujan pointed out that they have an asymptotic expansion at the cusps, similar to that of modular forms of weight , possibly with poles at cusps, but cannot be expressed in terms of "ordinary" theta functions. He called functions with similar properties "mock theta functions". Zwegers lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mock Theta Functions
In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight . The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his lost notebook. Sander Zwegers discovered that adding certain non-holomorphic functions to them turns them into harmonic weak Maass forms. History Ramanujan's 12 January 1920 letter to Hardy listed 17 examples of functions that he called mock theta functions, and his lost notebook contained several more examples. (Ramanujan used the term "theta function" for what today would be called a modular form.) Ramanujan pointed out that they have an asymptotic expansion at the cusps, similar to that of modular forms of weight , possibly with poles at cusps, but cannot be expressed in terms of "ordinary" theta functions. He called functions with similar properties "mock theta functions". Zwegers lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oosterhout
Oosterhout (; from ''ooster'', "eastern", and ''hout'', "woods") is a municipality and a city in the southern Netherlands. The municipality had a population of in . Population centers The municipality of Oosterhout includes the following places: History Oosterhout is mentioned for the first time in 1277, although archaeological excavations showed the existence of human settlements in the area in prehistoric times. The Knights Templar had a temple here dedicated to St. John the Baptist. It was home to a castle which later acquired control over the surrounding area, up to Breda and Bergen op Zoom. The castle was destroyed by Spanish troops during the Eighty Years War, in 1573; only a tower of it survives today. The city became the seat of a flourishing ceramics industry, which lasted until the 19th century. In 1625 the city was besieged by Frederick Henry, Prince of Orange, and suffered heavy damage. Despite the rise of Protestantism, it was home to several Catholic monast ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maass Form
In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup \Gamma of \mathrm_(\R) as modular forms. They are Eigenforms of the hyperbolic Laplace Operator \Delta defined on \mathbb and satisfy certain growth conditions at the cusps of a fundamental domain of \Gamma. In contrast to the modular forms the Maass forms need not be holomorphic. They were studied first by Hans Maass in 1949. General remarks The group : G := \mathrm_(\R) = \left\ operates on the upper half plane :\mathbb = \ by fractional linear transformations: :\begin a & b \\ c & d \\ \end \cdot z := \frac. It can be extended to an operation on \mathbb \cup \ \cup \mathbb by defining: :\begin a & b \\ c & d \\ \end\cdot z :=\begin \frac & \text cz+d \neq 0, \\ \infty & \text cz+d=0,\end :\begin a & b \\ c & d \\ \end \cdot \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Srinivasa Ramanujan
Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: according to Hans Eysenck: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal correspondence with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognising Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max-Planck Institute
The Max Planck Society for the Advancement of Science (german: Max-Planck-Gesellschaft zur Förderung der Wissenschaften e. V.; abbreviated MPG) is a formally independent non-governmental and non-profit association of German research institutes. Founded in 1911 as the Kaiser Wilhelm Society, it was renamed to the Max Planck Society in 1948 in honor of its former president, theoretical physicist Max Planck. The society is funded by the federal and state governments of Germany. Mission According to its primary goal, the Max Planck Society supports fundamental research in the natural, life and social sciences, the arts and humanities in its 86 (as of December 2018) Max Planck Institutes. The society has a total staff of approximately 17,000 permanent employees, including 5,470 scientists, plus around 4,600 non-tenured scientists and guests. The society's budget for 2018 was about €1.8 billion. As of December 31, 2018, the Max Planck Society employed a total of 23,767 staff, of wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University College Dublin
University College Dublin (commonly referred to as UCD) ( ga, Coláiste na hOllscoile, Baile Átha Cliath) is a public research university in Dublin, Ireland, and a collegiate university, member institution of the National University of Ireland. With 33,284 students, it is Ireland's largest university, and amongst the most prestigious universities in the country. Five Nobel Laureates are among UCD's alumni and current and former staff. Additionally, four Irish Taoiseach (Prime Ministers) and three Irish Presidents have graduated from UCD, along with one President of India. UCD originates in a body founded in 1854, which opened as the Catholic University of Ireland on the feast of Saint Malachy, St. Malachy with John Henry Newman as its first rector; it re-formed in 1880 and chartered in its own right in 1908. The Universities Act, 1997 renamed the constituent university as the "National University of Ireland, Dublin", and a ministerial order of 1998 renamed the institution as "U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Cologne
The University of Cologne (german: Universität zu Köln) is a university in Cologne, Germany. It was established in the year 1388 and is one of the most prestigious and research intensive universities in Germany. It was the sixth university to be established in Central Europe. It closed in 1798 before being re-established in 1919. It is now one of the largest universities in Germany with more than 48,000 students. The University of Cologne was a university of excellence as part of the German Universities Excellence Initiative from 2012 to 2019. As of 2021, 3 Nobel Prize winners have been affiliated with the university. Professors and former students have won 11 Leibniz Prizes, the most prestigious as well as the best-funded prize in Europe. History 1388–1798 The university of Cologne was established in 1388 as the fourth university in the Holy Roman Empire, after the Charles University of Prague (1348), the University of Vienna (1365) and the Ruprecht Karl University of H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lost Notebook
Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge. The "notebook" is not a book, but consists of loose and unordered sheets of paper described as "more than one hundred pages written on 138 sides in Ramanujan's distinctive handwriting. The sheets contained over six hundred mathematical formulas listed consecutively without proofs." have published several books in which they give proofs for Ramanujan's formulas included in the notebook. Berndt says of the notebook's discovery: "The discovery of this 'Lost Notebook' caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1975 Births
It was also declared the ''International Women's Year'' by the United Nations and the European Architectural Heritage Year by the Council of Europe. Events January * January 1 - Watergate scandal (United States): John N. Mitchell, H. R. Haldeman and John Ehrlichman are found guilty of the Watergate cover-up. * January 2 ** The Federal Rules of Evidence are approved by the United States Congress. ** Bangladesh revolutionary leader Siraj Sikder is killed by police while in custody. ** A bomb blast at Samastipur, Bihar, India, fatally wounds Lalit Narayan Mishra, Minister of Railways. * January 5 – Tasman Bridge disaster: The Tasman Bridge in Hobart, Tasmania, Australia, is struck by the bulk ore carrier , killing 12 people. * January 7 – OPEC agrees to raise crude oil prices by 10%. * January 10–February 9 – The flight of '' Soyuz 17'' with the crew of Georgy Grechko and Aleksei Gubarev aboard the '' Salyut 4'' space station. * January 15 – Alvor Agreem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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