In mathematics, p-adic analysis is a branch of number theory that studies functions of p-adic numbers. Along with the more classical fields of real and...

p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; p-adic numbers...

a constant field, and the harmonic oscillator. p-adic analysis Volovich, I. V. (1987-06-01). "p-adic space-time and string theory". Theoretical and Mathematical...

In mathematics, particularly p-adic analysis, the p-adic exponential function is a p-adic analogue of the usual exponential function on the complex numbers...

Fontaine's rings and p-adic L-functions (PDF) Koblitz, Neal (1984), p-adic Numbers, p-adic Analysis, and Zeta-Functions, Graduate Texts in Mathematics, vol. 58...

{\displaystyle \Gamma } isomorphic to the additive group of p-adic integers for some prime p. (These were called Γ {\displaystyle \Gamma } -extensions in...

notion of differentiability of functions that is particularly suited to p-adic analysis. In short, the definition is made more restrictive by allowing both...

mathematician who worked on the theory of Lie groups in the context of p-adic analysis. Born in Paris, Lazard studied at the University of Paris–Sorbonne...

In mathematics, the p-adic gamma function Γp is a function of a p-adic variable analogous to the gamma function. It was first explicitly defined by Morita...

In number theory, more specifically in p-adic analysis, Krasner's lemma is a basic result relating the topology of a complete non-archimedean field to...

the p-adic valuation or p-adic order of an integer n is the exponent of the highest power of the prime number p that divides n. It is denoted ν p ( n...

1998) was an American mathematician, known for his application of p-adic analysis to local zeta functions, and in particular for a proof of the first...

power of p tends to infinity, it follows that a root or a factorization modulo p can be lifted to a root or a factorization over the p-adic integers....

recherche at the CNRS (IMJ-PRG) known for his work in number theory and p-adic analysis. Colmez studied at École Normale Supérieure and obtained his doctorate...

In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions...

monogenic or Clifford analytic functions. p-adic analysis, the study of analysis within the context of p-adic numbers, which differs in some interesting...

real numbers, the complex numbers, and complete valued fields (such as the p-adic numbers). The real numbers are the field with the standard Euclidean metric...

of p-adic analysis, the Volkenborn integral is a method of integration for p-adic functions. Let : f : Z p → C p {\displaystyle f:\mathbb {Z} _{p}\to...

of Waterloo people Gross–Koblitz formula — (1984) [1977]. p-adic Numbers, p-adic Analysis, and Zeta-Functions. Graduate Texts in Mathematics. Vol. 58...

Yale University Press. p. 181. ISBN 978-0-300-21642-4. Robert, Alain M. (2000). A Course in p {\displaystyle p} -adic Analysis. Graduate Texts in Mathematics...

Patashnik 1994, p. 111. Caldwell & Xiong 2012, pp. 8–9. Kennedy 1974, pp. 389. Peano 1889, p. 1. Peano 1908, p. 27. Halmos 1974, p. 32. Hodges 2009, p. 14. Hext...

varieties. p-adic Hodge theory gives tools to examine when cohomological properties of varieties over the complex numbers extend to those over p-adic fields...

fields of transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers. Mahler was a student at the universities...

In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study p-adic Galois representations of characteristic 0 local fields...

theory p-adic analysis a branch of number theory that deals with the analysis of functions of p-adic numbers. p-adic dynamics an application of p-adic analysis...

fields were originally introduced in p-adic analysis since the fields Q p {\displaystyle \mathbb {Q} _{p}} of p-adic numbers are locally compact topological...

test is often checked first due to its ease of use. In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence...

– Israel Institute of Technology. He is known for his work in p-adic analysis, p-adic quantum mechanics, and non-additive geometry, including the field...

also be defined over fields of p {\displaystyle p} -adic numbers. This is part of p {\displaystyle p} -adic analysis. The prototypical example of a Banach...

Similar ideas can be found in domain theory. p-adic analysis makes heavy use of the ultrametric nature of the p-adic metric. In condensed matter physics, the...