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 25.8 points for quality (as of July 1, 2026). 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 (English) language version.

Since the creation of article “Maximum modulus principle”, its content was written by 55 registered users of English Wikipedia and edited by 139 registered Wikipedia users in all languages.

The article is cited 49 times in English Wikipedia and cited 133 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #50540 in March 2018
  • Global: #160354 in September 2012

The highest popularity rank from 2008:

  • Local (English): #280041 in April 2019
  • Global: #384215 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, 2026 (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
25.78
2Catalan (ca)
Principi del mòdul màxim
22.696
3Chinese (zh)
最大模原理
16.5485
4Korean (ko)
최대 절댓값 원리
15.9048
5Hebrew (he)
עקרון המקסימום
15.1842
6Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
12.1538
7Hungarian (hu)
Maximumelv
9.0302
8Russian (ru)
Принцип максимума модуля
7.57
9Ukrainian (uk)
Принцип максимуму модуля
6.8964
10Italian (it)
Teorema del massimo modulo
4.1716
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
439 956
2Russian (ru)
Принцип максимума модуля
42 092
3Japanese (ja)
最大絶対値の原理
37 913
4Spanish (es)
Principio del módulo máximo
32 308
5Hebrew (he)
עקרון המקסימום
28 439
6Chinese (zh)
最大模原理
27 942
7Italian (it)
Teorema del massimo modulo
21 024
8Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
7 580
9Korean (ko)
최대 절댓값 원리
7 363
10Hungarian (hu)
Maximumelv
1 057
More...

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

Most popular in June 2026

The most popular language versions of the article "Maximum modulus principle" in June 2026
#LanguagePopularity awardRelative popularity
1English (en)
Maximum modulus principle
1 263
2Chinese (zh)
最大模原理
118
3Russian (ru)
Принцип максимума модуля
109
4Japanese (ja)
最大絶対値の原理
90
5Spanish (es)
Principio del módulo máximo
82
6Italian (it)
Teorema del massimo modulo
52
7Hebrew (he)
עקרון המקסימום
50
8Korean (ko)
최대 절댓값 원리
13
9Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
13
10Catalan (ca)
Principi del mòdul màxim
7
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
55
2Russian (ru)
Принцип максимума модуля
20
3Italian (it)
Teorema del massimo modulo
19
4Hebrew (he)
עקרון המקסימום
13
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 2026

Language versions of the article "Maximum modulus principle" with the highest AI in June 2026
#LanguageAI awardRelative AI
1Catalan (ca)
Principi del mòdul màxim
0
2English (en)
Maximum modulus principle
0
3Spanish (es)
Principio del módulo máximo
0
4Hebrew (he)
עקרון המקסימום
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
49
2Hebrew (he)
עקרון המקסימום
38
3Turkish (tr)
Maksimum ilkesi (karmaşık analiz)
8
4Italian (it)
Teorema del massimo modulo
7
5Russian (ru)
Принцип максимума модуля
7
6Ukrainian (uk)
Принцип максимуму модуля
7
7Japanese (ja)
最大絶対値の原理
6
8Chinese (zh)
最大模原理
5
9Spanish (es)
Principio del módulo máximo
3
10Korean (ko)
최대 절댓값 원리
2
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2026:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2026:
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:
#280041
04.2019
Global:
#384215
10.2019

AI rank trends

Best Rank English:
#50540
03.2018
Global:
#160354
09.2012

Languages comparison

Important global interconnections (July 2025 – June 2026)

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

News from 1 July 2026

On 1 July 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: 2026 FIFA World Cup, Kylian Mbappé, Erling Haaland, Democratic Republic of the Congo, FIFA World Cup, Harry Kane, Romelu Lukaku, Senegal, Michael Olise, Sadio Mané.

In English Wikipedia the most popular articles on that day were: 2026 FIFA World Cup, Harry Kane, Julián Quiñones, List of FIFA World Cup top goalscorers, Kylian Mbappé, Democratic Republic of the Congo, Erling Haaland, DR Congo national football team, Melat Kiros, FIFA World Cup.

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 50 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2026. When calculating current popularity and AI of articles data from June 2026 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2026... More information