Wikipedia:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory

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This page provides a list of all articles available at PlanetMath in the following topic:

11-XX Number theory.

This list will be periodically updated. Each entry in the list has three fields:

  1. PM : The first field is the link to the PlanetMath article, along with the article's object ID.
  2. WP : The second field is either a "guessed" link to a correspondingly named Wikipedia article, produced by the script which generated the list, or one or more manually entered links to the corresponding Wikipedia articles on the subject.
  3. Status : The third field is the status field, which explains the current status of the entry. The recommended status entries are:
Status means PM article
N not needed
A adequately covered
C copied
M merged
NC needs copying
NM needs merging
  • Please update the WP and Status fields as appropriate.
  • if the WP field is correct please remove the qualifier "guess".
  • If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link.
  • If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry.
  • If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.

Don't forget to include the relevant template if you copy over text or feel like an external link is warranted

  • {{planetmath|id=|title=}} for copied over text
  • {{planetmath reference|id=|title=}} for an external link

See the main page for examples and usage criteria.

One can use the web-based program Pmform to convert PlanetMath articles to the Wikipedia format. As a side benefit, this tool will place the PlanetMath template for you.

11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)

AdamSmithee 09:31, 16 January 2006 (UTC)[reply]
CryptoDerk 14:29, May 2, 2005 (UTC)
CryptoDerk 14:47, May 2, 2005 (UTC)
There should also be a link to the method from Modular arithmetic - AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
Can be used to expand properties AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
CryptoDerk 17:41, May 2, 2005 (UTC)
CryptoDerk 17:58, May 2, 2005 (UTC)
linas 22:12, 12 Mar 2005 (UTC)
CryptoDerk 18:00, May 2, 2005 (UTC)
CryptoDerk 18:09, May 2, 2005 (UTC)
Hv 08:58, 5 August 2005 (UTC)[reply]
CryptoDerk 20:53, May 2, 2005 (UTC)
Charles Matthews 10:26, 25 October 2005 (UTC)[reply]
CryptoDerk 18:27, May 3, 2005 (UTC)
linas 23:53, 12 Mar 2005 (UTC)
Jeekc 11:25, 8 November 2005 (UTC)[reply]
Jeekc 11:25, 8 November 2005 (UTC)[reply]
Could use a remark on generalizing to gcd of more than 2 numbers AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
see also greatest common divisor - AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
linas 22:40, 12 Mar 2005 (UTC)
  • PM: mean, id=3028 -- WP: mean -- Status: A
Jeekc 11:25, 8 November 2005 (UTC)[reply]
AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
  • PM: pi, id=432 -- WP guess: pi -- Status:
AdamSmithee 09:31, 16 January 2006 (UTC)[reply]
AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
Hv 09:18, 5 August 2005 (UTC)[reply]
linas 00:34, 13 Mar 2005 (UTC)
Not a particularly illuminating proof AdamSmithee 13:02, 5 January 2006 (UTC)[reply]
AdamSmithee 15:35, 30 December 2005 (UTC)[reply]
AdamSmithee 13:02, 5 January 2006 (UTC)[reply]
CryptoDerk 22:20, Mar 12, 2005 (UTC)
linas 23:49, 12 Mar 2005 (UTC)
Charles Matthews 10:30, 25 October 2005 (UTC)[reply]
AdamSmithee 08:39, 8 March 2006 (UTC)[reply]
AdamSmithee 08:39, 8 March 2006 (UTC)[reply]

11-01 Instructional exposition (textbooks, tutorial papers, etc.)

Simon12 02:49, 30 July 2006 (UTC)[reply]
AdamSmithee 13:10, 5 January 2006 (UTC)[reply]

11A05 Multiplicative structure; Euclidean algorithm; greatest common divisors

linas 00:31, 13 Mar 2005 (UTC)
linas 23:18, 12 Mar 2005 (UTC)
linas 00:37, 13 Mar 2005 (UTC)
Jeekc 11:32, 8 November 2005 (UTC)[reply]
Jeekc 11:32, 8 November 2005 (UTC)[reply]
Jeekc 11:32, 8 November 2005 (UTC)[reply]
linas 23:24, 12 Mar 2005 (UTC)
linas 00:28, 13 Mar 2005 (UTC)
Can be used to clarify the affirmation in the WP article, which is already challenged in the Talk section AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
AdamSmithee 09:37, 16 January 2006 (UTC)[reply]
linas 00:40, 13 Mar 2005 (UTC)
linas 23:14, 12 Mar 2005 (UTC)

11A07 Congruences; primitive roots; residue systems

AdamSmithee 13:15, 5 January 2006 (UTC)[reply]
Hv 09:07, 5 August 2005 (UTC)[reply]
linas 22:37, 12 Mar 2005 (UTC)
Still needs TeX attention beyond my abilities. Jtwdog 17:33, 28 October 2005 (UTC)[reply]
PM article has a better wording than WP AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
linas 00:45, 13 Mar 2005 (UTC)

11A15 Power residues, reciprocity

linas 23:26, 12 Mar 2005 (UTC)
AdamSmithee 14:06, 5 January 2006 (UTC)[reply]
WP proof never actually shows that if a is not a quadratic residue mod p then a(p − 1)/2 ≡ −1 (mod p), so it could be combined with the PM proof AdamSmithee 14:06, 5 January 2006 (UTC)[reply]
linas 00:56, 13 Mar 2005 (UTC)

11A25 Arithmetic functions; related numbers; inversion formulas

AdamSmithee 14:23, 5 January 2006 (UTC)[reply]
linas 22:35, 12 Mar 2005 (UTC)
linas 22:55, 12 Mar 2005 (UTC)
Jtwdog 17:32, 28 October 2005 (UTC)[reply]
linas 22:57, 12 Mar 2005 (UTC)
linas 23:04, 12 Mar 2005 (UTC)
linas 23:01, 12 Mar 2005 (UTC)
PM has some more examples which could be used AdamSmithee 14:23, 5 January 2006 (UTC)[reply]
linas 23:11, 12 Mar 2005 (UTC)
Chenxlee (talk) 18:58, 25 September 2008 (UTC)[reply]
linas 01:14, 13 Mar 2005 (UTC)
WP redirect to be removed linas 23:08, 12 Mar 2005 (UTC)

11A41 Primes

linas 16:53, 4 July 2006 (UTC)[reply]
Composite elements of integral domains AdamSmithee 14:53, 5 January 2006 (UTC)[reply]
AdamSmithee 21:58, 30 December 2005 (UTC)[reply]
linas 00:58, 13 Mar 2005 (UTC)
linas 16:26, 4 July 2006 (UTC)[reply]
linas 00:58, 13 Mar 2005 (UTC)
linas 01:02, 13 Mar 2005 (UTC)
AdamSmithee 14:53, 5 January 2006 (UTC)[reply]
AdamSmithee 14:53, 5 January 2006 (UTC)[reply]
  • PM: emirp, id=9415new! -- WP guess: emirp -- Status:

11A51 Factorization; primality

linas 01:08, 13 Mar 2005 (UTC)

11A55 Continued fractions

linas 22:53, 12 Mar 2005 (UTC)
linas 22:51, 12 Mar 2005 (UTC)

11A63 Radix representation; digital problems

linas 01:12, 13 Mar 2005 (UTC)

11A67 Other representations

linas 23:39, 12 Mar 2005 (UTC)

11A99 Miscellaneous

linas 01:25, 13 Mar 2005 (UTC)

11Axx Elementary number theory

11B05 Density, gaps, topology

11B13 Additive bases

11B25 Arithmetic progressions

by Charles Matthews. Oleg Alexandrov 16:21, 15 July 2005 (UTC)[reply]

11B34 Representation functions

Chenxlee (talk) 19:01, 25 September 2008 (UTC)[reply]

11B37 Recurrences

CryptoDerk 22:25, Feb 1, 2005 (UTC)

11B39 Fibonacci and Lucas numbers and polynomials and generalizations

AdamSmithee 09:00, 8 March 2006 (UTC)[reply]
AdamSmithee 09:00, 8 March 2006 (UTC)[reply]
linas 03:27, 13 Mar 2005 (UTC)
I added an external link AdamSmithee 09:00, 8 March 2006 (UTC)[reply]
I added an external link AdamSmithee 09:00, 8 March 2006 (UTC)[reply]

11B50 Sequences (mod $m$)

11B57 Farey sequences; the sequences $$

11B65 Binomial coefficients; factorials; $q$-identities

11B68 Bernoulli and Euler numbers and polynomials

linas 01:19, 14 July 2005 (UTC)[reply]

11B73 Bell and Stirling numbers

11B75 Other combinatorial number theory

11B83 Special sequences and polynomials

11B85 Automata sequences

linas 02:13, 13 Mar 2005 (UTC)
minor merge, just copy the relation on the genering function.linas 02:13, 13 Mar 2005 (UTC)

11B99 Miscellaneous

linas 02:18, 13 Mar 2005 (UTC)
minor, just copy the table linas 02:16, 13 Mar 2005 (UTC)

11Bxx Sequences and sets

11C08 Polynomials

linas 02:21, 13 Mar 2005 (UTC)
Doctormatt 06:37, March 13, 2007 (UTC)

11C99 Miscellaneous

11Cxx Polynomials and matrices

11D09 Quadratic and bilinear equations

linas 01:17, 13 Mar 2005 (UTC)
linas 01:19, 13 Mar 2005 (UTC)

11D25 Cubic and quartic equations

11D41 Higher degree equations; Fermat's equation

linas 01:22, 13 Mar 2005 (UTC)

11D68 Rational numbers as sums of fractions

11D72 Equations in many variables

11D79 Congruences in many variables

AdamSmithee 09:54, 16 January 2006 (UTC)[reply]
AdamSmithee 09:54, 16 January 2006 (UTC)[reply]

11D85 Representation problems

11D99 Miscellaneous

easy merge, copy the stuff about algorithm linas 02:34, 13 Mar 2005 (UTC)

11Dxx Diophantine equations

11E04 Quadratic forms over general fields

11E08 Quadratic forms over local rings and fields

11E10 Forms over real fields

11E12 Quadratic forms over global rings and fields

11E16 General binary quadratic forms

11E25 Sums of squares and representations by other particular quadratic forms

11E39 Bilinear and Hermitian forms

11E57 Classical groups

11E76 Forms of degree higher than two

11E81 Algebraic theory of quadratic forms; Witt groups and rings

11E88 Quadratic spaces; Clifford algebras

copy the part about filter algebra linas 02:38, 13 Mar 2005 (UTC)

11Exx Forms and linear algebraic groups

11F06 Structure of modular groups and generalizations; arithmetic groups

The PM intro lends a nice concreteness to the abstract proceedings in WP. linas 02:43, 13 Mar 2005 (UTC)

11F11 Modular forms, one variable

linas 02:49, 13 Mar 2005 (UTC)
The redirect to Hecke operator should be undone. Or one could merge. linas 02:49, 13 Mar 2005 (UTC)
Why? Charles Matthews 19:53, 25 October 2005 (UTC)[reply]
linas 02:49, 13 Mar 2005 (UTC)

11F30 Fourier coefficients of automorphic forms

The PM article is badly mis-classified. linas 02:51, 13 Mar 2005 (UTC)

11F67 Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols

PM article is mis-classified linas 02:56, 13 Mar 2005 (UTC)
linas 02:59, 13 Mar 2005 (UTC)

11F80 Galois representations

11Fxx Discontinuous groups and automorphic forms

11G05 Elliptic curves over global fields

11G07 Elliptic curves over local fields

11Gxx Arithmetic algebraic geometry (Diophantine geometry)

11H06 Lattices and convex bodies

actually, just copy the graphic diagram over linas 03:01, 13 Mar 2005 (UTC)
The rigorous defn in PM is much nicer than the prose in WP. linas 03:04, 13 Mar 2005 (UTC)

11H46 Products of linear forms

11H55 Quadratic forms (reduction theory, extreme forms, etc.)

11Hxx Geometry of numbers

11J04 Homogeneous approximation to one number

11J06 Markov and Lagrange spectra and generalizations

11J61 Approximation in non-Archimedean valuations

11J68 Approximation to algebraic numbers

Chenxlee (talk) 02:19, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:27, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:30, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:30, 9 July 2008 (UTC)[reply]

11J70 Continued fractions and generalizations

11J71 Distribution modulo one

linas 03:06, 13 Mar 2005 (UTC)

11J72 Irrationality; linear independence over a field

Chenxlee (talk) 02:32, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:41, 9 July 2008 (UTC)[reply]
Chenxlee (talk) 02:41, 9 July 2008 (UTC)[reply]

11J81 Transcendence (general theory)

linas 01:36, 14 July 2005 (UTC)[reply]
KimJ, the owner of this article, mentioned to me that this was a joke entry. I concur. Even though it's true, this "theorem" doesn't go by this name except as a joke. CryptoDerk 02:48, Feb 2, 2005 (UTC)

11J82 Measures of irrationality and of transcendence

11J85 Algebraic independence; Gelfond's method

11J86 Linear forms in logarithms; Baker's method

11Jxx Diophantine approximation, transcendental number theory

11K06 General theory of distribution modulo $1$

11K16 Normal numbers, radix expansions, etc.

11K38 Irregularities of distribution, discrepancy

11K45 Pseudo-random numbers; Monte Carlo methods

11K99 Miscellaneous

11Kxx Probabilistic theory: distribution modulo $1$; metric theory of algorithms

11L03 Trigonometric and exponential sums, general

11L05 Gauss and Kloosterman sums; generalizations

linas 03:18, 13 Mar 2005 (UTC)
Jtwdog 17:57, 28 October 2005 (UTC)[reply]

11L40 Estimates on character sums

11Lxx Exponential sums and character sums

11M06 $\zeta (s)$ and $L(s, \chi)$

linas 22:47, 12 Mar 2005 (UTC)
linas 20:40, 2 June 2006 (UTC)[reply]
linas 22:49, 12 Mar 2005 (UTC)
linas 20:18, 2 June 2006 (UTC)[reply]

11M20 Real zeros of $L(s, \chi)$; results on $L(1, \chi)$

11M35 Hurwitz and Lerch zeta functions

11M41 Other Dirichlet series and zeta functions

11M99 Miscellaneous

11Mxx Zeta and $L$-functions: analytic theory

11N05 Distribution of primes

linas 03:40, 13 Mar 2005 (UTC)
linas 03:35, 13 Mar 2005 (UTC)
linas 03:42, 13 Mar 2005 (UTC)
linas 03:32, 13 Mar 2005 (UTC)

11N13 Primes in progressions

11N25 Distribution of integers with specified multiplicative constraints

11N32 Primes represented by polynomials; other multiplicative structure of polynomial values

AdamSmithee 15:35, 7 February 2006 (UTC)[reply]

11N35 Sieves

11N36 Applications of sieve methods

11N37 Asymptotic results on arithmetic functions

11N56 Rate of growth of arithmetic functions

11N80 Generalized primes and integers

11N99 Miscellaneous

11Nxx Multiplicative number theory

11P05 Waring's problem and variants

11P32 Goldbach-type theorems; other additive questions involving primes

11P81 Elementary theory of partitions

The PM article has a nice proof of the theorem. linas 01:28, 13 Mar 2005 (UTC)

11P99 Miscellaneous

11Pxx Additive number theory; partitions

11R04 Algebraic numbers; rings of algebraic integers

The PM article is more pleasently rigorous/clearer. linas 01:35, 13 Mar 2005 (UTC)
linas 01:32, 13 Mar 2005 (UTC)
It might be easier to just copy, and throw away the current WP article. linas 01:44, 13 Mar 2005 (UTC)
edited, actually ... the PM article is structured better, and is easier to read. linas 01:42, 13 Mar 2005 (UTC)

11R06 PV-numbers and generalizations; other special algebraic numbers

11R11 Quadratic extensions

11R16 Cubic and quartic extensions

11R18 Cyclotomic extensions

linas 01:46, 13 Mar 2005 (UTC)

11R20 Other abelian and metabelian extensions

11R21 Other number fields

11R27 Units and factorization

PM article is mis-categorized, needs to be with other p-adic topics linas 04:06, 13 Mar 2005 (UTC)

11R29 Class numbers, class groups, discriminants

Jtwdog 17:54, 28 October 2005 (UTC)[reply]
linas 01:49, 13 Mar 2005 (UTC)
Jtwdog 17:54, 28 October 2005 (UTC)[reply]
Jtwdog 17:54, 28 October 2005 (UTC)[reply]

11R32 Galois theory

Jeekc 11:35, 8 November 2005 (UTC)[reply]

11R34 Galois cohomology

11R37 Class field theory

11R42 Zeta functions and $L$-functions of number fields

11R44 Distribution of prime ideals

11R45 Density theorems

11R52 Quaternion and other division algebras: arithmetic, zeta functions

11R56 Adèle rings and groups

linas 03:47, 13 Mar 2005 (UTC)
linas 03:49, 13 Mar 2005 (UTC)

11R58 Arithmetic theory of algebraic function fields

11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)

11R99 Miscellaneous

linas 04:00, 13 Mar 2005 (UTC)
linas 04:00, 13 Mar 2005 (UTC)
linas 04:00, 13 Mar 2005 (UTC)
linas 04:00, 13 Mar 2005 (UTC)
linas 03:54, 13 Mar 2005 (UTC)

11Rxx Algebraic number theory: global fields

11S15 Ramification and extension theory

11S20 Galois theory

11S25 Galois cohomology

11S31 Class field theory; $p$-adic formal groups

11S80 Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.)

11S99 Miscellaneous

11Sxx Algebraic number theory: local and $p$-adic fields

11T23 Exponential sums

11T30 Structure theory

11T55 Arithmetic theory of polynomial rings over finite fields

11T71 Algebraic coding theory; cryptography

11T99 Miscellaneous

11Txx Finite fields and commutative rings (number-theoretic aspects)

11Y05 Factorization

11Y11 Primality

11Y40 Algebraic number theory computations

11Y55 Calculation of integer sequences

11Y65 Continued fraction calculations

11Y99 Miscellaneous

11Yxx Computational number theory

11Z05 Miscellaneous applications of number theory

linas 22:21, 12 Mar 2005 (UTC)
Charles Matthews 10:48, 25 October 2005 (UTC)[reply]
Charles Matthews 10:48, 25 October 2005 (UTC)[reply]
Charles Matthews 10:49, 25 October 2005 (UTC)[reply]
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