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Hans Petersson
Hans Petersson (24 September 1902 in Bentschen – 9 November 1984 in Münster) was a German mathematician. He introduced the Petersson inner product and is also known for the Ramanujan–Petersson conjecture In mathematics, the Ramanujan conjecture, due to , states that Ramanujan's tau function given by the Fourier coefficients of the cusp form of weight :\Delta(z)= \sum_\tau(n)q^n=q\prod_\left (1-q^n \right)^ = q-24q^2+252q^3- 1472q^4 + 4830q^5-\ .... See also * Weil–Petersson metric References * * {{DEFAULTSORT:Petersson, Hans 1902 births 1984 deaths People from Zbąszyń 20th-century German mathematicians People from the Province of Posen Academic staff of Charles University Nazi Party members Academic staff of the University of Münster ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Münster
Münster (; nds, Mönster) is an independent city (''Kreisfreie Stadt'') in North Rhine-Westphalia, Germany. It is in the northern part of the state and is considered to be the cultural centre of the Westphalia region. It is also a state district capital. Münster was the location of the Anabaptist rebellion during the Protestant Reformation and the site of the signing of the Treaty of Westphalia ending the Thirty Years' War in 1648. Today it is known as the bicycle capital of Germany. Münster gained the status of a ''Großstadt'' (major city) with more than 100,000 inhabitants in 1915. , there are 300,000 people living in the city, with about 61,500 students, only some of whom are recorded in the official population statistics as having their primary residence in Münster. Münster is a part of the international Euregio region with more than 1,000,000 inhabitants (Enschede, Hengelo, Gronau, Osnabrück). History Early history In 793, Charlemagne sent out Ludger as a miss ... [...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] |
Petersson Inner Product
In mathematics the Petersson inner product is an inner product defined on the space of entire modular forms. It was introduced by the German mathematician Hans Petersson. Definition Let \mathbb_k be the space of entire modular forms of weight k and \mathbb_k the space of cusp forms. The mapping \langle \cdot , \cdot \rangle : \mathbb_k \times \mathbb_k \rightarrow \mathbb, :\langle f , g \rangle := \int_\mathrm f(\tau) \overline (\operatorname\tau)^k d\nu (\tau) is called Petersson inner product, where :\mathrm = \left\ is a fundamental region of the modular group \Gamma and for \tau = x + iy :d\nu(\tau) = y^dxdy is the hyperbolic volume form. Properties The integral is absolutely convergent and the Petersson inner product is a positive definite Hermitian form. For the Hecke operators T_n, and for forms f,g of level \Gamma_0, we have: :\langle T_n f , g \rangle = \langle f , T_n g \rangle This can be used to show that the space of cusp forms of level \Gamma_0 has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramanujan–Petersson Conjecture
In mathematics, the Ramanujan conjecture, due to , states that Ramanujan's tau function given by the Fourier coefficients of the cusp form of weight :\Delta(z)= \sum_\tau(n)q^n=q\prod_\left (1-q^n \right)^ = q-24q^2+252q^3- 1472q^4 + 4830q^5-\cdots, where q=e^, satisfies :, \tau(p), \leq 2p^, when is a prime number. The generalized Ramanujan conjecture or Ramanujan–Petersson conjecture, introduced by , is a generalization to other modular forms or automorphic forms. Ramanujan L-function The Riemann zeta function and the Dirichlet L-function satisfy the Euler product, and due to their completely multiplicative property Are there L-functions other than the Riemann zeta function and the Dirichlet L-functions satisfying the above relations? Indeed, the L-functions of automorphic forms satisfy the Euler product (1) but they do not satisfy (2) because they do not have the completely multiplicative property. However, Ramanujan discovered that the L-function of the mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weil–Petersson Metric
In mathematics, the Weil–Petersson metric is a Kähler metric on the Teichmüller space ''T''''g'',''n'' of genus ''g'' Riemann surfaces with ''n'' marked points. It was introduced by using the Petersson inner product on forms on a Riemann surface (introduced by Hans Petersson). Definition If a point of Teichmüller space is represented by a Riemann surface ''R'', then the cotangent space at that point can be identified with the space of quadratic differentials at ''R''. Since the Riemann surface has a natural hyperbolic metric, at least if it has negative Euler characteristic, one can define a Hermitian inner product on the space of quadratic differentials by integrating over the Riemann surface. This induces a Hermitian inner product on the tangent space to each point of Teichmüller space, and hence a Riemannian metric. Properties stated, and proved, that the Weil–Petersson metric is a Kähler metric. proved that it has negative holomorphic sectional, scalar, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1902 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipkn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1984 Deaths
Events January * January 1 – The Bornean Sultanate of Brunei gains full independence from the United Kingdom, having become a British protectorate in 1888. * January 7 – Brunei becomes the sixth member of the Association of Southeast Asian Nations (ASEAN). * January 10 ** The United States and the Vatican (Holy See) restore full diplomatic relations. ** The Victoria Agreement is signed, institutionalising the Indian Ocean Commission. *January 24 – Steve Jobs launches the Macintosh personal computer in the United States. February * February 3 ** Dr. John Buster and the research team at Harbor–UCLA Medical Center announce history's first embryo transfer from one woman to another, resulting in a live birth. ** STS-41-B: Space Shuttle ''Challenger'' is launched on the 10th Space Shuttle mission. * February 7 – Astronauts Bruce McCandless II and Robert L. Stewart make the first untethered space walk. * February 8– 19 – The 1984 Winter Olympics are held i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Zbąszyń
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From The Province Of Posen
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academic Staff Of Charles University
An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary or tertiary higher learning (and generally also research or honorary membership). The name traces back to Plato's school of philosophy, founded approximately 385 BC at Akademia, a sanctuary of Athena, the goddess of wisdom and skill, north of Athens, Greece. Etymology The word comes from the ''Academy'' in ancient Greece, which derives from the Athenian hero, ''Akademos''. Outside the city walls of Athens, the gymnasium was made famous by Plato as a center of learning. The sacred space, dedicated to the goddess of wisdom, Athena, had formerly been an olive grove, hence the expression "the groves of Academe". In these gardens, the philosopher Plato conversed with followers. Plato developed his sessions into a method of teaching philosophy and in 387 BC, established what is known today as the Old Academy. By extension, ''academia'' has come to mean the accumulation, dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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