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Incubator escapee wiki:WikiProject Mathematics/PlanetMath Exchange/11-XX Number theory

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

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

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

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

11A05 Multiplicative structure; Euclidean algorithm; greatest common divisorsEdit

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)
Jeekc 11:32, 8 November 2005 (UTC)
Jeekc 11:32, 8 November 2005 (UTC)
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)
AdamSmithee 09:37, 16 January 2006 (UTC)
linas 00:40, 13 Mar 2005 (UTC)
linas 23:14, 12 Mar 2005 (UTC)

11A07 Congruences; primitive roots; residue systemsEdit

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

11A15 Power residues, reciprocityEdit

linas 23:26, 12 Mar 2005 (UTC)
AdamSmithee 14:06, 5 January 2006 (UTC)
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)
linas 00:56, 13 Mar 2005 (UTC)

11A25 Arithmetic functions; related numbers; inversion formulasEdit

AdamSmithee 14:23, 5 January 2006 (UTC)
linas 22:35, 12 Mar 2005 (UTC)
linas 22:55, 12 Mar 2005 (UTC)
Jtwdog 17:32, 28 October 2005 (UTC)
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)
linas 23:11, 12 Mar 2005 (UTC)
Chenxlee (talk) 18:58, 25 September 2008 (UTC)
linas 01:14, 13 Mar 2005 (UTC)
WP redirect to be removed linas 23:08, 12 Mar 2005 (UTC)

11A41 PrimesEdit

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

11A51 Factorization; primalityEdit

linas 01:08, 13 Mar 2005 (UTC)

11A55 Continued fractionsEdit

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

11A63 Radix representation; digital problemsEdit

linas 01:12, 13 Mar 2005 (UTC)

11A67 Other representationsEdit

linas 23:39, 12 Mar 2005 (UTC)

11A99 MiscellaneousEdit

linas 01:25, 13 Mar 2005 (UTC)

11Axx Elementary number theoryEdit

11B05 Density, gaps, topologyEdit

11B13 Additive basesEdit

11B25 Arithmetic progressionsEdit

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

11B34 Representation functionsEdit

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

11B37 RecurrencesEdit

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

11B39 Fibonacci and Lucas numbers and polynomials and generalizationsEdit

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

11B50 Sequences (mod $m$)Edit

11B57 Farey sequences; the sequences $$Edit

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

11B68 Bernoulli and Euler numbers and polynomialsEdit

linas 01:19, 14 July 2005 (UTC)

11B73 Bell and Stirling numbersEdit

11B75 Other combinatorial number theoryEdit

11B83 Special sequences and polynomialsEdit

11B85 Automata sequencesEdit

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 MiscellaneousEdit

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

11Bxx Sequences and setsEdit

11C08 PolynomialsEdit

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

11C99 MiscellaneousEdit

11Cxx Polynomials and matricesEdit

11D09 Quadratic and bilinear equationsEdit

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

11D25 Cubic and quartic equationsEdit

11D41 Higher degree equations; Fermat's equationEdit

linas 01:22, 13 Mar 2005 (UTC)

11D68 Rational numbers as sums of fractionsEdit

11D72 Equations in many variablesEdit

11D79 Congruences in many variablesEdit

AdamSmithee 09:54, 16 January 2006 (UTC)
AdamSmithee 09:54, 16 January 2006 (UTC)

11D85 Representation problemsEdit

11D99 MiscellaneousEdit

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

11Dxx Diophantine equationsEdit

11E04 Quadratic forms over general fieldsEdit

11E08 Quadratic forms over local rings and fieldsEdit

11E10 Forms over real fieldsEdit

11E12 Quadratic forms over global rings and fieldsEdit

11E16 General binary quadratic formsEdit

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

11E39 Bilinear and Hermitian formsEdit

11E57 Classical groupsEdit

11E76 Forms of degree higher than twoEdit

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

11E88 Quadratic spaces; Clifford algebrasEdit

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

11Exx Forms and linear algebraic groupsEdit

11F06 Structure of modular groups and generalizations; arithmetic groupsEdit

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

11F11 Modular forms, one variableEdit

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)
linas 02:49, 13 Mar 2005 (UTC)

11F30 Fourier coefficients of automorphic formsEdit

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 symbolsEdit

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

11F80 Galois representationsEdit

11Fxx Discontinuous groups and automorphic formsEdit

11G05 Elliptic curves over global fieldsEdit

11G07 Elliptic curves over local fieldsEdit

11Gxx Arithmetic algebraic geometry (Diophantine geometry)Edit

11H06 Lattices and convex bodiesEdit

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 formsEdit

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

11Hxx Geometry of numbersEdit

11J04 Homogeneous approximation to one numberEdit

11J06 Markov and Lagrange spectra and generalizationsEdit

11J61 Approximation in non-Archimedean valuationsEdit

11J68 Approximation to algebraic numbersEdit

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

11J70 Continued fractions and generalizationsEdit

11J71 Distribution modulo oneEdit

linas 03:06, 13 Mar 2005 (UTC)

11J72 Irrationality; linear independence over a fieldEdit

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

11J81 Transcendence (general theory)Edit

linas 01:36, 14 July 2005 (UTC)
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 transcendenceEdit

11J85 Algebraic independence; Gelfond's methodEdit

11J86 Linear forms in logarithms; Baker's methodEdit

11Jxx Diophantine approximation, transcendental number theoryEdit

11K06 General theory of distribution modulo $1$Edit

11K16 Normal numbers, radix expansions, etc.Edit

11K38 Irregularities of distribution, discrepancyEdit

11K45 Pseudo-random numbers; Monte Carlo methodsEdit

11K99 MiscellaneousEdit

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

11L03 Trigonometric and exponential sums, generalEdit

11L05 Gauss and Kloosterman sums; generalizationsEdit

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

11L40 Estimates on character sumsEdit

11Lxx Exponential sums and character sumsEdit

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

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

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

11M35 Hurwitz and Lerch zeta functionsEdit

11M41 Other Dirichlet series and zeta functionsEdit

11M99 MiscellaneousEdit

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

11N05 Distribution of primesEdit

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 progressionsEdit

11N25 Distribution of integers with specified multiplicative constraintsEdit

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

AdamSmithee 15:35, 7 February 2006 (UTC)

11N35 SievesEdit

11N36 Applications of sieve methodsEdit

11N37 Asymptotic results on arithmetic functionsEdit

11N56 Rate of growth of arithmetic functionsEdit

11N80 Generalized primes and integersEdit

11N99 MiscellaneousEdit

11Nxx Multiplicative number theoryEdit

11P05 Waring's problem and variantsEdit

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

11P81 Elementary theory of partitionsEdit

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

11P99 MiscellaneousEdit

11Pxx Additive number theory; partitionsEdit

11R04 Algebraic numbers; rings of algebraic integersEdit

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 numbersEdit

11R11 Quadratic extensionsEdit

11R16 Cubic and quartic extensionsEdit

11R18 Cyclotomic extensionsEdit

linas 01:46, 13 Mar 2005 (UTC)

11R20 Other abelian and metabelian extensionsEdit

11R21 Other number fieldsEdit

11R27 Units and factorizationEdit

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, discriminantsEdit

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

11R32 Galois theoryEdit

Jeekc 11:35, 8 November 2005 (UTC)

11R34 Galois cohomologyEdit

11R37 Class field theoryEdit

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

11R44 Distribution of prime idealsEdit

11R45 Density theoremsEdit

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

11R56 Adèle rings and groupsEdit

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

11R58 Arithmetic theory of algebraic function fieldsEdit

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

11R99 MiscellaneousEdit

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 fieldsEdit

11S15 Ramification and extension theoryEdit

11S20 Galois theoryEdit

11S25 Galois cohomologyEdit

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

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

11S99 MiscellaneousEdit

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

11T23 Exponential sumsEdit

11T30 Structure theoryEdit

11T55 Arithmetic theory of polynomial rings over finite fieldsEdit

11T71 Algebraic coding theory; cryptographyEdit

11T99 MiscellaneousEdit

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

11Y05 FactorizationEdit

11Y11 PrimalityEdit

11Y40 Algebraic number theory computationsEdit

11Y55 Calculation of integer sequencesEdit

11Y65 Continued fraction calculationsEdit

11Y99 MiscellaneousEdit

11Yxx Computational number theoryEdit

11Z05 Miscellaneous applications of number theoryEdit

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