Synonymer & Information om | Engelska ordet P-ADIC

Exempel på hur man kan använda P-ADIC i en mening

• Many other fields, such as fields of rational functions, algebraic function fields, algebraic number fields, and p-adic fields are commonly used and studied in mathematics, particularly in number theory and algebraic geometry.
• He introduced the theory of buildings (sometimes known as Tits buildings), which are combinatorial structures on which groups act, particularly in algebraic group theory (including finite groups, and groups defined over the p-adic numbers).
• In England he did postgraduate research at the University of Cambridge, his doctoral dissertation being on p-adic analogues of Baker's method.
• The same ideas are often applied to Lie groups, Lie algebras, algebraic groups and p-adic number analogues, making it harder to summarise the facts into a unified theory.
• The latter begin from the Bernoulli numbers, and use interpolation to define p-adic analogues of the Dirichlet L-functions.
• Grothendieck used étale cohomology to prove some of the Weil conjectures (Bernard Dwork had already managed to prove the rationality part of the conjectures in 1960 using p-adic methods), and the remaining conjecture, the analogue of the Riemann hypothesis was proved by Pierre Deligne (1974) using ℓ-adic cohomology.
• Earlier (1965) work of Michel Lazard, whose importance was not appreciated by the specialists in the field for about 20 years, had dealt with the case where K is the ring of p-adic integers and G is the pth congruence subgroup of.
• Given a polynomial equation with rational coefficients, if it has a rational solution, then this also yields a real solution and a p-adic solution, as the rationals embed in the reals and p-adics: a global solution yields local solutions at each prime.
• Work of Roger Howe in the 1970s and his papers with Allen Moy on representations of p-adic GL(n) opened a possibility of classifying irreducible admissible representations of reductive groups over local fields in terms of appropriately constructed Hecke algebras.
• Nicholas Michael Katz (born December 7, 1943) is an American mathematician, working in arithmetic geometry, particularly on p-adic methods, monodromy and moduli problems, and number theory.
• Cassels often studied individual Diophantine equations by algebraic number theory and p-adic methods.
• Powerful p-groups are also useful in the study of pro-p groups as it provides a simple means for characterising p-adic analytic groups (groups that are manifolds over the p-adic numbers): A finitely generated pro-p group is p-adic analytic if and only if it contains an open normal subgroup that is powerful: this is a special case of a deep result of Michel Lazard (1965).
• calls this notation k-adic, but it should not be confused with the p-adic numbers: bijective numerals are a system for representing ordinary integers by finite strings of nonzero digits, whereas the p-adic numbers are a system of mathematical values that contain the integers as a subset and may need infinite sequences of digits in any numerical representation.
• Flicker's research interests include Automorphic and Admissible Representations, Automorphic forms over function fields, Arithmetic Geometry, Lifting of Representations, Hecke-Iwahori algebras, p-adic automorphic forms, Galois Cohomology, Local-Global Principles, Motives, Algebraic Groups, Covering Groups, Shimura Varieties.
• David Roberts provided a natural combinatorial link between the Artin–Hasse exponential and the regular exponential in the spirit of the ergodic perspective (linking the p-adic and regular norms over the rationals) by showing that the Artin–Hasse exponential is also the generating function for the probability that an element of the symmetric group is unipotent in characteristic p, whereas the regular exponential is the probability that an element of the same group is unipotent in characteristic zero.
• In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence due to the non-Archimedean ultrametric triangle inequality.
• In 1976, he proved a result on quantifier elimination for p-adic fields from which a theory of semi-algebraic and subanalytic geometry for p-adic fields follows (in analogy with that for the real field) as shown by Jan Denef and Lou van den Dries and others.
• Coleman is also known for introducing p-adic Banach spaces into the study of modular forms and discovering important classicality criteria for overconvergent p-adic modular forms.
• This is because p-adic series converge if and only if the summands tend to zero, and since the n! in the denominator of each summand tends to make them large p-adically, a small value of z is needed in the numerator.
• Kummer's work on the congruences for the class numbers of cyclotomic fields was generalized in the twentieth century by Iwasawa in Iwasawa theory and by Kubota and Leopoldt in their theory of p-adic zeta functions.

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