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| 1 | P |
| , blackboard bold represents the prime numbers In the Metric system, p, Pico, is an SI prefix meaning 10 -12... Latin alphabet A B C D E F G H I J K L M N O P Q R S T U V W X Y Z P is the... Etruscan and Latin letters that developed from the former alphabet all symbolized /p/, a plosive, unvoiced ... | |
| 2 | P-adic analysis |
| P-adic analysis ( p-adic analysis) is a branch of mathematics that deals with functions of p-adic numbers. P-adic analysis concerns how functional solutions are related to rational solutions. It... generalization and extension. P-adic analysis is used in probability theory, number theory, algebraic ... | |
| 3 | P-adic number |
| For every prime number p , the p -adic numbers form an extension field of the rational numbers... the p -adic numbers for every prime p . The space Q p of all p -adic numbers has the nice topological.... Motivation If p is a fixed prime number, then any integer can be written as a p-adic expansion ... | |
| 4 | Topological ring |
| algebras are topological rings. The rational, real, complex and p -adic numbers are also topological... -adic topology on R : a subset U of R is open iff for every x in U there exists a natural number n such... only if the intersection of all powers of I is the zero ideal (0). The p -adic topology on the ... | |
| 5 | Number system |
| A number system is a set of objects on which arithmetic operations can be performed. Examples of number systems are: the real numbers, the rational numbers, the algebraic numbers, the complex numbers, the p-adic numbers, the surreal numbers, the hyperreal numbers. Whether, for example, the ... | |
| 6 | Chowla-Selberg formula |
| particular the analogue for p-adic numbers, involving a p-adic gamma function, was initiated by Gross and Koblitz; and is important in the theory of p-adic periods ... | |
| 7 | Hypercomplex number |
| | Sedenions | Hyperreal numbers | Surreal numbers | Ordinal numbers | Cardinal numbers | p -adic numbers... In mathematics, hypercomplex numbers are extensions of the complex numbers constructed by means of abstract algebra, such as quaternions, octonions and sedenions. Whereas complex numbers can be ... | |
| 8 | Jacques Tits |
| group theory (including finite groups, and groups defined over the p-adic numbers). The related... Jacques Tits (born August 12, 1930) is a Belgian mathematician. He has written and cowritten a large number of papers on a number of subjects, principally algebra. He introduced the theory of ... | |
| 9 | Integer sequence |
| numbers | p -adic numbers | Integer sequences | Mathematical constants | Infinity... received their own name include: Catalan numbers Euler numbers Fibonacci numbers Figurate numbers Lucas numbers Topics in mathematics related to quantity Numbers | Natural numbers | Integers ... | |
| 10 | John Tate |
| algebraic K-theory. He made a number of individual and important contributions to p-adic theory: the Lubin...' parametrisation for p-adic elliptic curves; p-divisible (Tate-Barsotti) groups. Many of his..., distinguished for many fundamental contributions in algebraic number theory and related areas in ... | |
| 11 | Iwasawa theory |
| group of p-adic integers. That group, usually written Γ in the theory and with multiplicative... /p n. Z, where p is the fixed prime number and n = 1,2, ... . We can express this by Pontryagin... numbers. A first and important example is in terms of the field K = Q (ζ) with ζ a primitive p -th ... | |
| 12 | Class field theory |
| field of rational numbers the structure of G is an infinite product of the additive group of p-adic integers (see p-adic numbers) taken over all prime numbers p, and of a product of infinitely many... Class field theory is a branch of algebraic number theory, including most of the major results ... | |
| 13 | Hasse principle |
| assertion that an equation can be solved over the rational numbers if and only if it can be solved over the real numbers and over the p -adic numbers for every prime p . The Hasse-Minkowski theorem states that the local-global principle holds for quadratic forms over the rational numbers (which is ... | |
| 14 | Rational number |
| numbers are the completion of Q . p -adic numbers In addition to the absolute value metric mentioned above... completion is the p -adic number field Q p. See also: integer -- irrational number -- real number... numbers | p -adic numbers | Integer sequences | Mathematical constants | Infinity ... | |
| 15 | John Coates |
| research at the University of Cambridge, his doctoral dissertation being on p -adic analogues of... Fermat's Last Theorem - in which Coates's work on elliptic curves, Iwasawa theory, and p -adic L... fundamental research in number theory and for his many contributions to mathematical life both in the UK and ... |