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 China 392 works
- 2 United States 298 works
- 3 India 249 works
- 4 Türkiye 101 works
- 5 Japan 96 works
- 6 South Korea 83 works
- 7 France 79 works
- 8 Canada 68 works
- 9 Germany 60 works
- 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.
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 Indian Institute of Technology KharagpurIndia 33 works
- 2 Zhoukou Normal UniversityChina 17 works
- 3 Akdeniz UniversityTürkiye 16 works
- 4 Suzhou University of Science and TechnologyChina 16 works
- 5 Northwest UniversityChina 15 works
- 6 Centre National de la Recherche ScientifiqueFrance 15 works
- 7 Kwangwoon UniversitySouth Korea 14 works
- 8 Prince Mohammad bin Fahd UniversitySaudi Arabia 13 works
- 9 Aligarh Muslim UniversityIndia 13 works
- 10 York UniversityCanada 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 Stephan Ramon Garcia United States 4k citations
- 2 G. N. Watson United Kingdom 3.6k citations
- 3 Terence Tao United States 3.1k citations
- 4 N. J. A. Sloane United States 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
Where it is the local speciality
- KharagpurIN · 33.2 works34×
Location quotient: how much more of its research is in Advanced Mathematical Identities than the world average.
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.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Sogang UniversitySouth Korea | 67.7 | 74.9% | 68.5× | 11 | +20.6% |
| 2 | Kwangwoon UniversitySouth Korea | 67.6 | 72.1% | 98.7× | 14 | -0.5% |
| 3 | Aligarh Muslim UniversityIndia | 63.2 | 36.5% | 23.8× | 12 | +121.1% |
| 4 | Prince Mohammad bin Fahd UniversitySaudi Arabia | 62.5 | 36.8% | 105.7× | 13 | — |
| 5 | Suzhou University of Science and TechnologyChina | 56.5 | 37.1% | 37.2× | 16 | — |
| 6 | Akdeniz UniversityTürkiye | 54.0 | 22.9% | 40.6× | 16 | +57.2% |
| 7 | York UniversityCanada | 52.1 | 11.2% | 16.1× | 11 | +113.9% |
| 8 | Indian Institute of Technology KharagpurIndia | 51.7 | 0.3% | 33.6× | 33 | — |
| 9 | University of CologneGermany | 49.2 | 26.9% | 16.7× | 10 | +18.0% |
| 10 | Zhoukou Normal UniversityChina | 48.8 | 15.9% | 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.
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.