Link budget: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Patrick
→‎In radio systems: (geometric spreading)
Removed a stray period at the end of the first paragraph
 
Line 1: Line 1:
In [[mathematics]], '''Eisenstein's theorem''', named after the German mathematician [[Gotthold Eisenstein]], applies to the coefficients of any [[power series]] which is an [[algebraic function]] with [[rational number]] coefficients. Through the theorem, it is readily demonstrable that a function such as the [[exponential function]] must be a [[transcendental function]].  
I woke up yesterday  and realized - I've been solitary for a while at the moment and following much bullying from buddies I now locate myself signed up for on line dating. They guaranteed me that there are a lot of pleasant, regular and interesting individuals to fulfill, so the pitch is gone by here!<br>I strive to keep as physically healthy as possible being at the gymnasium several-times weekly. I love my athletics and attempt to perform or see while many a possible. Being winter I shall frequently at Hawthorn suits. Note: If you [http://photo.net/gallery/tag-search/search?query_string=considered+purchasing considered purchasing] a sport I don't brain, I've observed the carnage of wrestling suits at stocktake sales.<br>My friends and family are  [http://lukebryantickets.lazintechnologies.com luke bryan shows] amazing and spending time with them at pub gigs or dinners is obviously vital. I haven't ever been in to clubs as I discover you can do not get a significant conversation with the noise. I likewise have 2 unquestionably cheeky and really cunning dogs who are almost always ready to meet new people.<br><br><br><br>Here is my webpage  [http://lukebryantickets.pyhgy.com tickets to see luke bryan] - [http://lukebryantickets.iczmpbangladesh.org luke bryan 2014 tour schedule]
 
Suppose therefore that
 
:<math>\sum_{}^{} a_n t^n</math>
 
is a [[formal power series]] with rational coefficients ''a''<sub>''n''</sub>, which has a non-zero [[radius of convergence]] in the [[complex plane]], and within it represents an [[analytic function]] that is in fact an algebraic function. Let ''d''<sub>''n''</sub> denote the [[denominator]] of ''a''<sub>''n''</sub>, as a fraction [[in lowest terms]]. Then Eisenstein's theorem states that there is a finite set ''S'' of [[prime number]]s ''p'', such that every prime factor of a number ''d''<sub>''n''</sub> is contained in ''S''.
 
This has an interpretation in terms of [[p-adic number]]s: with an appropriate extension of the idea, the ''p''-adic radius of convergence of the series is at least 1, for [[almost all]] ''p'' (i.e. the primes outside the finite set ''S''). In fact that statement is a little weaker, in that it disregards any initial [[partial sum]] of the series, in a way that may ''vary'' according to ''p''. For the other primes the radius is non-zero.
 
Eisenstein's original paper is the short communication
''Über eine allgemeine Eigenschaft der Reihen-Entwicklungen aller algebraischen Functionen''
(1852), reproduced in Mathematische Gesammelte Werke, Band II, Chelsea Publishing Co., New York, 1975,
p.&nbsp;765–767.
 
More recently, many authors have investigated precise and effective bounds quantifying the above [[almost all]].
See, e.g.,  Sections 11.4 and 11.55 of the book by E. Bombieri & W. Gubler.
 
==References==
*{{Cite book|last = Bombieri|first = Enrico|authorlink=Enrico Bombieri|coauthors = [[Walter Gubler|Gubler, Walter]]|section=A local Eisenstein theorem|section=Power series, norms, and the local Eisenstein theorem|title=Heights in Diophantine Geometry|publisher=Cambridge University Press|year=2008|pages=362&ndash;376|doi= 10.2277/0521846153}}
 
{{DEFAULTSORT:Eisenstein's Theorem}}
[[Category:Theorems in number theory]]

Latest revision as of 00:33, 28 October 2014

I woke up yesterday and realized - I've been solitary for a while at the moment and following much bullying from buddies I now locate myself signed up for on line dating. They guaranteed me that there are a lot of pleasant, regular and interesting individuals to fulfill, so the pitch is gone by here!
I strive to keep as physically healthy as possible being at the gymnasium several-times weekly. I love my athletics and attempt to perform or see while many a possible. Being winter I shall frequently at Hawthorn suits. Note: If you considered purchasing a sport I don't brain, I've observed the carnage of wrestling suits at stocktake sales.
My friends and family are luke bryan shows amazing and spending time with them at pub gigs or dinners is obviously vital. I haven't ever been in to clubs as I discover you can do not get a significant conversation with the noise. I likewise have 2 unquestionably cheeky and really cunning dogs who are almost always ready to meet new people.



Here is my webpage tickets to see luke bryan - luke bryan 2014 tour schedule

Retrieved from "https://en.formulasearchengine.com/index.php?title=Link_budget&oldid=240642"