Science Explorer Interactive view Map

Advanced Mathematical Identities

Advanced Mathematical Identities is a research topic within Algebra and Number Theory. Science Explorer counts 13k research works in it since 1950. 16.3% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the arithmetic properties, modular forms, q-series, and supercongruences related to multiple zeta values. It explores Ramanujan-type formulas, harmonic maass forms, and motivic periods in the context of number theory.

  • Multiple Zeta Values
  • Modular Forms
  • q-Series
  • Supercongruences
  • Polylogarithms
  • Partition Function
  • Ramanujan-Type Formulas
  • Harmonic Maass Forms
  • Motivic Periods
  • Number Theory
Research works
13k
fractional, since 1950
In the world top 10%
2.1k
per year above
Top-10% rate
16.3%
share of its works in the world top 10%
Growth, 2013–17 → 2018–22
+12%
the tick is no change

Which countries lead Advanced Mathematical Identities research?

By volume, China and the United States publish the most (392 and 298 works in 2022–2025).

By volume, 2022–2025

  1. 1 China 392 works
  2. 2 United States 298 works
  3. 3 India 249 works
  4. 4 Türkiye 101 works
  5. 5 Japan 96 works
  6. 6 South Korea 83 works
  7. 7 France 79 works
  8. 8 Canada 68 works
  9. 9 Germany 60 works
  10. 10 Russia 49 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: 26.6%United States: 20.2%India: 16.9%Türkiye: 6.9%6 others listed: 29.5%27%largest
China392 · 26.6%United States298 · 20.2%India249 · 16.9%Türkiye101 · 6.9%6 others listed435 · 29.5%

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

Which institutions lead Advanced Mathematical Identities research?

By volume in 2022–2025, Indian Institute of Technology Kharagpur publishes the most Advanced Mathematical Identities research, followed by Zhoukou Normal University and Akdeniz University.

By volume, 2022–2025

  1. 1 Indian Institute of Technology Kharagpur India 33 works
  2. 2 Zhoukou Normal University China 17 works
  3. 3 Akdeniz University Türkiye 16 works
  4. 4 Suzhou University of Science and Technology China 16 works
  5. 5 Northwest University China 15 works
  6. 6 Centre National de la Recherche Scientifique France 15 works
  7. 7 Kwangwoon University South Korea 14 works
  8. 8 Prince Mohammad bin Fahd University Saudi Arabia 13 works
  9. 9 Aligarh Muslim University India 13 works
  10. 10 York University Canada 11 works

Who are the leading researchers in Advanced Mathematical Identities?

The most-cited researchers publishing on Advanced Mathematical Identities include Stephan Ramon Garcia, G. N. Watson and Terence Tao.

  1. 1 Stephan Ramon Garcia 4k citations
  2. 2 G. N. Watson 3.6k citations
  3. 3 Terence Tao 3.1k citations
  4. 4 N. J. A. Sloane 2.8k citations

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

Where is Advanced Mathematical Identities research done?

The largest centres of Advanced Mathematical Identities research in 2022–2025 are Seoul (South Korea), Kharagpur (India), Nanjing (China) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Kharagpur.

Largest cities, 2022–2025

  1. 1 Seoul South Korea 48 works
  2. 2 Kharagpur India 33 works
  3. 3 Nanjing China 30 works
  4. 4 Tokyo Japan 30 works
  5. 5 Paris France 29 works
  6. 6 Moscow Russia 28 works
  7. 7 Shanghai China 28 works
  8. 8 Xi'an China 27 works
  9. 9 Hangzhou China 25 works
  10. 10 Tianjin China 23 works

Where it is the local speciality

  1. KharagpurIN · 33.2 works34×
← less than its size predictsmore →

Location quotient: how much more of its research is in Advanced Mathematical Identities than the world average.

See Advanced Mathematical Identities on the map

Where is the best place to study Advanced Mathematical Identities?

Among universities, judged by research, Sogang University, Kwangwoon University and Aligarh Muslim University 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%50%100%mean 33.46%fractional works in this node (log) →share in the world top 10% →Sogang University: 11, 74.9%Kwangwoon University: 14, 72.1%Aligarh Muslim University: 12, 36.5%Prince Mohammad bin Fahd University: 13, 36.8%Suzhou University of Science and Technology: 16, 37.1%Akdeniz University: 16, 22.9%York University: 11, 11.2%Indian Institute of Technology Kharagpur: 33, 0.3%University of Cologne: 10, 26.9%Zhoukou Normal University: 17, 15.9%Sogang UniversityKwangwoon UniversityPrince Mohammad bin …Aligarh Muslim Unive…
above the meannear itbelow it

One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.

#UniversityScoreTop 10%SpecialisationWorksGrowth
1Sogang University South Korea 67.774.9%68.5×11 +20.6%
2Kwangwoon University South Korea 67.672.1%98.7×14 -0.5%
3Aligarh Muslim University India 63.236.5%23.8×12 +121.1%
4Prince Mohammad bin Fahd University Saudi Arabia 62.536.8%105.7×13
5Suzhou University of Science and Technology China 56.537.1%37.2×16
6Akdeniz University Türkiye 54.022.9%40.6×16 +57.2%
7York University Canada 52.111.2%16.1×11 +113.9%
8Indian Institute of Technology Kharagpur India 51.70.3%33.6×33
9University of Cologne Germany 49.226.9%16.7×10 +18.0%
10Zhoukou Normal University China 48.815.9%219.0×17

Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.

Is Advanced Mathematical Identities research growing?

Output in 2018–2022 was 12% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Advanced Mathematical Identities.

19801990200020102020
grewheldshrank

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

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.