Anagram & Information om | Engelska ordet ZETA

Exempel på hur man kan använda ZETA i en mening

• The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function.
• The free Riemann gas has a number of other interesting connections to number theory, including the fact that the partition function is the Riemann zeta function.
• Questions in number theory are often best understood through the study of analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory).
• The Riemann zeta function plays a pivotal role in analytic number theory and has applications in physics, probability theory, and applied statistics.
• In most English-speaking countries, including Australia, Canada, India, Ireland, New Zealand, South Africa and the United Kingdom, the letter's name is zed , reflecting its derivation from the Greek letter zeta (this dates to Latin, which borrowed Y and Z from Greek), but in American English its name is zee , analogous to the names for B, C, D, etc.
• In mathematics, a zeta function is (usually) a function analogous to the original example, the Riemann zeta function.
• The ratio of the zeta functions is well-defined, even for n > s − 1 because the series representation of the zeta function can be analytically continued.
• The Laurent series expansion for the Riemann zeta function*, where it is the first of the Stieltjes constants.
• Weil conjectured that such zeta functions for smooth varieties are rational functions, satisfy a certain functional equation, and have their zeros in restricted places.
• The Weil conjectures about zeta functions of varieties over finite fields, proved by Dwork, Grothendieck, Deligne and others.
• The Riemann zeta function is an example of an L-function, and some important conjectures involving L-functions are the Riemann hypothesis and its generalizations.

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