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ZetaGrid
ZetaGrid was at one time the largest distributed computing project, designed to explore the non-trivial roots of the Riemann zeta function, checking over one billion roots a day. Roots of the zeta function are of particular interest in mathematics, since the presence of even a single one that is out of line with the rest would disprove the Riemann hypothesis, with far-reaching consequences for all of mathematics. So far, every single one of them has failed to provide a counterexample to the Riemann hypothesis. The project ended in November 2005 due to instability of the hosting provider. Over 1013 first zeroes were checked.Ed Pegg Jr''«Ten Trillion Zeta Zeros»''/ref> After the results were analyzed, the project administrator were posted on the 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 comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Hypothesis
In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by , after whom it is named. The Riemann hypothesis and some of its generalizations, along with Goldbach's conjecture and the twin prime conjecture, make up Hilbert's eighth problem in David Hilbert's list of twenty-three unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems, which offers a million dollars to anyone who solves any of them. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields. The Riemann zeta function ζ(''s'') is a function whose argument ''s'' may be any complex number ... [...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] |
Distributed Computing
A distributed system is a system whose components are located on different computer network, networked computers, which communicate and coordinate their actions by message passing, passing messages to one another from any system. Distributed computing is a field of computer science that studies distributed systems. The components of a distributed system interact with one another in order to achieve a common goal. Three significant challenges of distributed systems are: maintaining concurrency of components, overcoming the clock synchronization, lack of a global clock, and managing the independent failure of components. When a component of one system fails, the entire system does not fail. Examples of distributed systems vary from service-oriented architecture, SOA-based systems to massively multiplayer online games to peer-to-peer, peer-to-peer applications. A computer program that runs within a distributed system is called a distributed program, and ''distributed programming' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root Of A Function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) ''vanishes'' at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. A "zero" of a function is thus an input value that produces an output of 0. A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by f(x)=x^2-5x+6 has the two roots (or zeros) that are 2 and 3. f(2)=2^2-5\times 2+6= 0\textf(3)=3^2-5\times 3+6=0. If the function maps real numbers to real numbers, then it ... [...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 ... [...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] |
Grid Computing
Grid computing is the use of widely distributed computer resources to reach a common goal. A computing grid can be thought of as a distributed system with non-interactive workloads that involve many files. Grid computing is distinguished from conventional high-performance computing systems such as cluster computing in that grid computers have each node set to perform a different task/application. Grid computers also tend to be more heterogeneous and geographically dispersed (thus not physically coupled) than cluster computers. Although a single grid can be dedicated to a particular application, commonly a grid is used for a variety of purposes. Grids are often constructed with general-purpose grid middleware software libraries. Grid sizes can be quite large. Grids are a form of distributed computing composed of many networked loosely coupled computers acting together to perform large tasks. For certain applications, distributed or grid computing can be seen as a special type of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeta And L-functions
Zeta (, ; uppercase Ζ, lowercase ζ; grc, ζῆτα, el, ζήτα, label=Demotic Greek, classical or ''zē̂ta''; ''zíta'') is the sixth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 7. It was derived from the Phoenician letter zayin . Letters that arose from zeta include the Roman Z and Cyrillic З. Name Unlike the other Greek letters, this letter did not take its name from the Phoenician letter from which it was derived; it was given a new name on the pattern of beta, eta and theta. The word ''zeta'' is the ancestor of ''zed'', the name of the Latin letter Z in Commonwealth English. Swedish and many Romanic languages (such as Italian and Spanish) do not distinguish between the Greek and Roman forms of the letter; "''zeta''" is used to refer to the Roman letter Z as well as the Greek letter. Uses Letter The letter ζ represents the voiced alveolar fricative in Modern Greek. The sound represented by zeta in Greek before 400&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert's Problems
Hilbert's problems are 23 problems in mathematics published by German mathematician David Hilbert in 1900. They were all unsolved at the time, and several proved to be very influential for 20th-century mathematics. Hilbert presented ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21, and 22) at the Paris conference of the International Congress of Mathematicians, speaking on August 8 at the University of Paris, Sorbonne. The complete list of 23 problems was published later, in English translation in 1902 by Mary Frances Winston Newson in the ''Bulletin of the American Mathematical Society''. Earlier publications (in the original German) appeared in and Nature and influence of the problems Hilbert's problems ranged greatly in topic and precision. Some of them, like the 3rd problem, which was the first to be solved, or the 8th problem (the Riemann hypothesis), which still remains unresolved, were presented precisely enough to enable a clear affirmative or negative answer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
