Maximum modulus principle

en

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Maximum modulus principle

Quality:

Maximum modulus principle - theorem that a holomorphic function’s absolute value cannot reach a strict local maximum at the interior of its domain. Article "Maximum modulus principle" in English Wikipedia has 22.9 points for quality (as of July 1, 2025). The article contains 1 references and 11 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

In June 2025 the article "Maximum modulus principle" was edited by 1 authors in English Wikipedia and written by 3 authors in all languages.

Since the creation of article "Maximum modulus principle", its content was written by 53 registered users of English Wikipedia and edited by 134 registered Wikipedia users in all languages.

The article is cited 31 times in English Wikipedia and cited 112 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #50507 in March 2018
  • Global: #160176 in September 2012

The highest popularity rank from 2008:

  • Local (English): #278921 in April 2019
  • Global: #382881 in October 2019

There are 12 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Maximum modulus principle
22.9363
2Catalan (ca)
Principi del mòdul màxim
22.5057
3Chinese (zh)
最大模原理
16.5593
4Korean (ko)
최대 절댓값 원리
15.9509
5Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
12.1289
6Hungarian (hu)
Maximumelv
9.0321
7Russian (ru)
Принцип максимума модуля
7.5579
8Hebrew (he)
עקרון המקסימום
7.1294
9Ukrainian (uk)
Принцип максимуму модуля
6.9371
10Italian (it)
Teorema del massimo modulo
4.1554
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Maximum modulus principle" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Maximum modulus principle
418 807
2Russian (ru)
Принцип максимума модуля
38 949
3Japanese (ja)
最大絶対値の原理
36 743
4Spanish (es)
Principio del módulo máximo
31 245
5Hebrew (he)
עקרון המקסימום
27 567
6Chinese (zh)
最大模原理
26 518
7Italian (it)
Teorema del massimo modulo
20 354
8Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
7 451
9Korean (ko)
최대 절댓값 원리
7 028
10Hungarian (hu)
Maximumelv
989
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Maximum modulus principle" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Maximum modulus principle
2 147
2Russian (ru)
Принцип максимума модуля
190
3Spanish (es)
Principio del módulo máximo
152
4Japanese (ja)
最大絶対値の原理
137
5Chinese (zh)
最大模原理
124
6Hebrew (he)
עקרון המקסימום
118
7Italian (it)
Teorema del massimo modulo
96
8Korean (ko)
최대 절댓값 원리
58
9Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
36
10Catalan (ca)
Principi del mòdul màxim
13
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Maximum modulus principle" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Maximum modulus principle
53
2Italian (it)
Teorema del massimo modulo
19
3Russian (ru)
Принцип максимума модуля
19
4Hebrew (he)
עקרון המקסימום
11
5Spanish (es)
Principio del módulo máximo
7
6Japanese (ja)
最大絶対値の原理
7
7Ukrainian (uk)
Принцип максимуму модуля
5
8Chinese (zh)
最大模原理
5
9Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
4
10Hungarian (hu)
Maximumelv
2
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Maximum modulus principle" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Hebrew (he)
עקרון המקסימום
2
2English (en)
Maximum modulus principle
1
3Catalan (ca)
Principi del mòdul màxim
0
4Spanish (es)
Principio del módulo máximo
0
5Hungarian (hu)
Maximumelv
0
6Italian (it)
Teorema del massimo modulo
0
7Japanese (ja)
最大絶対値の原理
0
8Korean (ko)
최대 절댓값 원리
0
9Russian (ru)
Принцип максимума модуля
0
10Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Maximum modulus principle" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Maximum modulus principle
31
2Hebrew (he)
עקרון המקסימום
13
3Korean (ko)
최대 절댓값 원리
12
4Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
12
5Spanish (es)
Principio del módulo máximo
9
6Italian (it)
Teorema del massimo modulo
7
7Japanese (ja)
最大絶対値の原理
7
8Russian (ru)
Принцип максимума модуля
7
9Ukrainian (uk)
Принцип максимуму модуля
7
10Chinese (zh)
最大模原理
6
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
caCatalan
Principi del mòdul màxim
enEnglish
Maximum modulus principle
esSpanish
Principio del módulo máximo
heHebrew
עקרון המקסימום
huHungarian
Maximumelv
itItalian
Teorema del massimo modulo
jaJapanese
最大絶対値の原理
koKorean
최대 절댓값 원리
ruRussian
Принцип максимума модуля
trTurkish
Maksimum ilkesi (karmaşık analiz)
ukUkrainian
Принцип максимуму модуля
zhChinese
最大模原理

Popularity rank trends

Best Rank English:
#278921
04.2019
Global:
#382881
10.2019

AI rank trends

Best Rank English:
#50507
03.2018
Global:
#160176
09.2012

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Maximum modulus principle from Wikipedia articles about Maximum principle, Schwarz lemma, Fundamental theorem of algebra, Harmonic function and Open mapping theorem. Whereas reading the article about Maximum modulus principle people most often go to Wikipedia articles on Schwarz lemma, Open mapping theorem, Holomorphic function, Cauchys integral formula and Maximum principle.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

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About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information