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Topic · Applied Mathematics

Meromorphic and Entire Functions

Meromorphic and Entire Functions is a research topic within Applied Mathematics. Science Explorer counts 9.7k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on complex differential equations, meromorphic functions, and their properties such as value distribution, uniqueness theorems, and normal families. It also explores topics related to difference equations, Nevanlinna theory, and the growth estimates of solutions.

  • Meromorphic Functions
  • Difference Equations
  • Value Distribution Theory
  • Uniqueness Theorems
  • Nevanlinna Theory
  • Normal Families
  • Linear Differential Equations
  • Weighted Sharing
  • Entire Solutions
  • Growth Estimates
Research works
9.7k
fractional, since 1950
In the world top 10%
976
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+6%
the tick is no change
Largest producer
China
27% of the 10 largest, 2022-now
Meromorphic and Entire Functions

Which countries lead Meromorphic and Entire Functions research?

By volume, China and India publish the most (224 and 206 works in 2022-now).

By volume, 2022-now

  1. 1 China 224 works
  2. 2 India 206 works
  3. 3 United States 110 works
  4. 4 Russia 77 works
  5. 5 Japan 47 works
  6. 6 France 46 works
  7. 7 Ukraine 45 works
  8. 8 Vietnam 32 works
  9. 9 Spain 24 works
  10. 10 Germany 24 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 26.8%India: 24.7%United States: 13.2%Russia: 9.2%6 others listed: 26.2%27%largest
China224 · 26.8%India206 · 24.7%United States110 · 13.2%Russia77 · 9.2%6 others listed219 · 26.2%

Shares of the rows listed above, not of the whole node.

Which institutions lead Meromorphic and Entire Functions research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Meromorphic and Entire Functions research, followed by University of Kalyani and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 24 works
  2. 2 University of KalyaniIndia 23 works
  3. 3 Russian Academy of SciencesRussia 19 works
  4. 4 Lviv UniversityUkraine 16 works
  5. 5 Université de MostaganemAlgeria 14 works
  6. 6 Raiganj UniversityIndia 13 works
  7. 7 Bangalore UniversityIndia 11 works
  8. 8 Nanchang UniversityChina 11 works
  9. 9 Fujian Normal UniversityChina 9 works
  10. 10 Lomonosov Moscow State UniversityRussia 9 works

Who are the leading researchers in Meromorphic and Entire Functions?

The most-cited researchers publishing on Meromorphic and Entire Functions include Hywel C Williams and John A. Todd.

  1. 1 Hywel C Williams United Kingdom 126k citations
  2. 2 John A. Todd United Kingdom 107k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Meromorphic and Entire Functions?

The most cited paper in Meromorphic and Entire Functions is "Existence of minimal models for varieties of log general type" (Caucher Birkar, Paolo Cascini, Christopher D. Hacon et al., 2009), with 1,375 citations. Next come "Theory of Functions of a Complex Variable" (1,243) and "Meromorphic Functions" (1,219).

Most cited papers
#PaperReleasedCitations
1 Existence of minimal models for varieties of log general type Caucher Birkar, Paolo Cascini, Christopher D. Hacon et al. · Journal of the American Mathematical Society Open access 13 Nov 2009 1,375
2 Theory of Functions of a Complex Variable A. I. Markushevich, Richard A. Silverman, James T. Gillis · Physics Today Jun 1966 1,243
3 Meromorphic Functions Walter Kurt Hayman, Eleanor F. Lingham · Problem books in mathematics Book chapter 2019 1,219
4 On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises Christophe Breuil, Brian Conrad, Fred Diamond et al. · Journal of the American Mathematical Society Open access 15 May 2001 791
5 Elementary and Analytic Theory of Algebraic Numbers Peter Shiu, Władysław Narkiewicz · The Mathematical Gazette Oct 1991 769
All 99 most cited papers, with filters and sorting

Where is Meromorphic and Entire Functions research done?

The largest centres of Meromorphic and Entire Functions research in 2022-now are Moscow (Russia), Beijing (China), Lviv (Ukraine) and Hanoi (Vietnam). Among places with at least 20 works in it, it is an unusually large share of all research in Kalyani and Lviv.

Largest cities, 2022-now

  1. 1 MoscowRussia 33 works
  2. 2 BeijingChina 30 works
  3. 3 LvivUkraine 24 works
  4. 4 HanoiVietnam 23 works
  5. 5 KalyaniIndia 23 works
  6. 6 KolkataIndia 22 works
  7. 7 BengaluruIndia 17 works
  8. 8 NanchangChina 17 works
  9. 9 TokyoJapan 15 works
  10. 10 MostaganemAlgeria 14 works

Where it is the local speciality

  1. KalyaniIN · 22.7 works161×
  2. LvivUA · 23.5 works29×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Meromorphic and Entire Functions than the world average.

See Meromorphic and Entire Functions on the map

Where is the best place to study Meromorphic and Entire Functions?

Among universities, judged by research, Nanchang University, Lviv University and University of Kalyani score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%5%10%15%mean 6.16667%fractional works in this field (log) →share of work in the world top 10% →Nanchang UniversityLviv UniversityRaiganj UniversityUniversity of Kalyani
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Nanchang UniversityChina 66.712.5%14.1×11 +11.9%
2Lviv UniversityUkraine 54.712.0%122.0×16 -14.3%
3University of KalyaniIndia 48.82.7%204.8×23 -30.5%
4Raiganj UniversityIndia 43.26.0%422.0×13 +69.1%
5Université de MostaganemAlgeria 43.02.8%387.2×14 +15.2%
6Lomonosov Moscow State UniversityRussia 40.713.3%10.0×9 +116.2%
7Fujian Normal UniversityChina 38.05.1%40.5×9 +216.5%
8Bangalore UniversityIndia 28.40.0%130.9×11 +65.4%
9Vidyasagar UniversityIndia 13.91.1%99.7×8 -12.1%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Meromorphic and Entire Functions, country by country

Is Meromorphic and Entire Functions research growing?

Output in 2022-2025 was 6% higher than in 2018-2021, peaking in 2011. The fastest-growing topics are Meromorphic and Entire Functions.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Meromorphic and Entire Functions as a percentage of every work published that year, 0.0047% in 2024.

still counting0.010%0.020%0.030%Meromorphic and Entire Functions0.0046% in 202519801990200020102020

Fractional works of Meromorphic and Entire Functions over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Meromorphic and Entire Functions10.7% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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