What is the p-adic metric?
A -adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime are related to proximity in the so called ” -adic metric.”
What is a p-adic group?
In mathematics, the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
What is the purpose of p-adic numbers?
The p-adic absolute value gives us a new way to measure the distance between two numbers. The p-adic distance between two numbers x and y is the p-adic absolute value of the number x-y.
What is the meaning of modular forms?
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. …
What is ADIC math?
Filters. (1) See AIDC. 1. (mathematics computing) When combined with prefixes derived (usually) from Latin or Greek names for numbers, used to make adjectives meaning “having a certain number of arguments” (said of functions, relations, etc, in mathematics and functions, operators, etc, in computing).
Is the P-ADIC integers complete?
The p-adic integers can also be seen as the completion of the integers with respect to a p-adic metric. Let us introduce a p-adic valuation on the integers, which we will extend to Zp.
What is the meaning of ADIC?
What is an ADIC space?
Adic spaces are the basic objects in Huber’s approach to non-archimedean analytic geometry. They are built by gluing valuation spectra? of a certain class of topological rings. Unlike Berkovich analytic spectra the points of adic spaces correspond to valuations of arbitrary rank, not only rank one.
Who invented p-adic numbers?
mathematician Kurt Hensel
The p-adic numbers were invented at the beginning of the twentieth century by the German mathematician Kurt Hensel (1861–1941). The aim was to make the methods of power series expansions, which play such a dominant role in the theory of functions, available to the theory of numbers as well.
Why are modular forms called modular?
Technically, if the weight is k, then it’s a differential k-form on the folded space. This is where the name comes from. The folded space is a modular curve, and the function is a differential form. Hence: modular form.
Who discovered modular forms?
The first modular forms (of level 4, not level 1) were found by Gauss in his work on the arithmetic-geometric mean around 1800, and it would take until the end of the 19th century for the term “modular form” to be introduced, in 1890.
What is ADIC?
Abu Dhabi Investment Council (ADIC) is a sovereign wealth fund owned by the government of Abu Dhabi, the capital city of the United Arab Emirates (UAE). The Abu Dhabi Investment Authority (ADIA), one of the world’s largest sovereign wealth funds, spun of ADIC in 2007.