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In [[algebraic number theory]], a '''supersingular prime''' is a [[prime number]] with a certain relationship to a given [[elliptic curve]]. If the curve ''E'' defined over the [[rational number]]s, then a prime ''p'' is '''supersingular for ''E''''' if the [[Good reduction#G|reduction]] of ''E'' modulo&nbsp;''p'' is a [[supersingular elliptic curve]] over the [[residue field]]&nbsp;'''F'''<sub>p</sub>.
If you have one thing Search Engine Marketers and site owners fear - it&quot;s a major protocol upgrade, specially by Google. Well, much as we might enjoy it not to occur, its here. Google has recently done a major formula update, nick called Jagger update series. <br><br>


{{Harvtxt|Elkies|1987}} showed that any elliptic curve over the rational numbers has infinitely many supersingular primes. However, the set of supersingular primes has asymptotic density zero. {{harvtxt|Lang|Trotter|1976}} conjectured that the number of supersingular primes less than a bound ''X'' is within a constant multiple of <math>\frac{\sqrt{X}}{ln X}</math>, using heuristics involving the distribution of [[Frobenius eigenvalue]]s. {{As of|2012}}, this conjecture is open.
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More generally, if ''K'' is any [[global field]]—i.e., a [[finite extension]] either of '''Q''' or of '''F'''<sub>p</sub>(''t'')—and ''A'' is an [[abelian variety]] defined over ''K'', then a '''supersingular prime <math>\mathfrak{p}</math> for ''A''''' is a [[finite place]] of ''K'' such that the reduction of ''A'' modulo <math>\mathfrak{p}</math> is a supersingular [[abelian variety]].
 
== References ==
*{{cite journal |authorlink=Noam Elkies |first=Noam D. |last=Elkies |title=The existence of infinitely many supersingular primes for every elliptic curve over '''Q''' |journal=[[Inventiones Mathematicae|Invent. Math.]] |volume=89 |year=1987 |issue=3 |pages=561–567 |doi=10.1007/BF01388985 |ref=harv }}
*{{cite book |last=Lang |first=Serge |authorlink1=Serge Lang|last2=Trotter |first2=Hale F. |authorlink2=Hale F. Trotter|year=1976 |title=Frobenius distributions in GL<sub>2</sub>-extensions |location=New York |publisher=[[Springer-Verlag]] |isbn=0-387-07550-X | zbl=0329.12015 | series=Lecture Notes in Mathematics | volume=504 | ref=harv }}
*{{cite book |authorlink=Andrew Ogg |last=Ogg |first=A. P. |chapter=Modular Functions |title=The Santa Cruz Conference on Finite Groups. Held at the University of California, Santa Cruz, Calif., June 25–July 20, 1979 |editor1-first=Bruce |editor1-last=Cooperstein |editor2-first=Geoffrey |editor2-last=Mason |location=Providence, RI |publisher=[[American Mathematical Society]] |pages=521–532 |year=1980 |isbn=0-8218-1440-0 | zbl=0448.10021 | series=Proc. Symp. Pure Math. | volume=37 }}
*{{cite book | authorlink = Joseph H. Silverman |first=Joseph H. |last=Silverman | year = 1986 | title = The Arithmetic of Elliptic Curves | publisher = [[Springer-Verlag]] |location=New York |isbn=0-387-96203-4 | zbl=0585.14026 | series=[[Graduate Texts in Mathematics]] | volume=106 }}
 
{{Prime number classes}}
 
[[Category:Classes of prime numbers]]
[[Category:Algebraic number theory]]
[[Category:Unsolved problems in mathematics]]

Revision as of 01:15, 28 February 2014

If you have one thing Search Engine Marketers and site owners fear - it"s a major protocol upgrade, specially by Google. Well, much as we might enjoy it not to occur, its here. Google has recently done a major formula update, nick called Jagger update series.

Google does slight algorithm updates very nearly on a regular basis and once in a little while, it uses a significant algorithm update. The final important Google protocol update occurred in November 2003 called the Florida update, which made quite a stir with internet site ranks. To know more, read our report o-n Google Florida Algo Update.

Such as the Florida update, the Jagger update has done the much feared blender work. It has churned the top-ranking internet sites and made it into a list of unrecognizable pulp.

Google is a hot-favorite amongst the net area looking for information. Most believe that the search engine results have been very appropriate. It"d be for that reason safe to assume that what-ever formula Google has, works just fine. So why does Google need to re-engineer its perfect-looking algo so drastically? Has it not heard the old saying do not repair what aint broke? From Google"s point of view, the reason is straightforward and appropriate. Well, to begin with, net is ever-evolving and the algo often need to be altered to be able to provide the best of results. Google engineered an algo, which it believes will reward good sites and rank them well for its audiences.

Google, similar to other search engines, keeps this algo a carefully guarded secret to prevent it from being used. Nevertheless, the SEO area is constantly at work wanting to rank their sites well. Using determined guesswork, logical thinking, special tests and extensive trial-and-error techniques, they gradually figure out what the algorithm likes and dislikes. Be taught extra info on the affiliated wiki - Hit this web site: http://www.tyler-collins.com/. Armed with this information, it"s not difficult to work on websites to rank them full of SERP (Se Result Pages), whether the site deserves to rank at the top or not. Dig up extra info on this related site by clicking sponsor. This sort of algorithm abuse leads to less-than desirable" websites displacing great sites from-the top ranks, damaging the Google index. Consequently, after the Kaizen philosophy, Google needs to re-engineer its calculations to keep, what it thinks are poor sites, out-of its top ranks. So that you can begin once again naturally, significant protocol improvements upset the current high-ranking web sites & sends plenty of Search Engine Optimisation specialists back-to their work-bench. Webaddress contains further about the meaning behind this enterprise.

What is interesting to see may be the timing of the protocol update. When Google updated its algorithm in November 2003, there were large-scale allegations by internet site owners that Google intentionally upset the ranks of common websites right before the Christmas shopping season to drive them into getting Google AdWords paid advertising in order to support visitors traffic. While Google promises that the algo update decisions are not influenced by the AdWords staff, it"s difficult to realize why they would once more pick a important moment right before Christmas buying season to update their protocol. The stakes are extremely large and its business after all. Google earned $1.57 Billion in Q3 of 2005. If 2003 pre-Christmas formula upgrade result is any sign, I estimate that Google would record earnings of around $2.05 Billion in Q4 of 2005..

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