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Topic · Algebra and Number Theory

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. 10.2% 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%
1.3k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+13%
the tick is no change
Largest producer
China
27% of the 10 largest, 2022-now
Advanced Mathematical Identities

Which countries lead Advanced Mathematical Identities research?

By volume, China and the United States publish the most (454 and 360 works in 2022-now).

By volume, 2022-now

  1. 1 China 454 works
  2. 2 United States 360 works
  3. 3 India 287 works
  4. 4 Türkiye 110 works
  5. 5 Japan 109 works
  6. 6 France 93 works
  7. 7 South Korea 89 works
  8. 8 Canada 74 works
  9. 9 Germany 72 works
  10. 10 Russia 52 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: 26.7%United States: 21.2%India: 16.9%Türkiye: 6.5%6 others listed: 28.8%27%largest
China454 · 26.7%United States360 · 21.2%India287 · 16.9%Türkiye110 · 6.5%6 others listed489 · 28.8%

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

Which institutions lead Advanced Mathematical Identities research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Mathematical Identities research, followed by Indian Institute of Technology Kharagpur and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 48 works
  2. 2 Indian Institute of Technology KharagpurIndia 38 works
  3. 3 Russian Academy of SciencesRussia 19 works
  4. 4 Akdeniz UniversityTürkiye 18 works
  5. 5 Zhoukou Normal UniversityChina 18 works
  6. 6 Suzhou University of Science and TechnologyChina 17 works
  7. 7 Northwest UniversityChina 16 works
  8. 8 Kwangwoon UniversitySouth Korea 15 works
  9. 9 Prince Mohammad bin Fahd UniversitySaudi Arabia 14 works
  10. 10 Aligarh Muslim UniversityIndia 13 works

Who are the leading researchers in Advanced Mathematical Identities?

The most-cited researchers publishing on Advanced Mathematical Identities include Stephen M. Smith, Y. Yang and Hywel C Williams.

  1. 1 Stephen M. Smith United Kingdom 214k citations
  2. 2 Y. Yang Israel 128k citations
  3. 3 Hywel C Williams United Kingdom 126k 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 Advanced Mathematical Identities?

The most cited paper in Advanced Mathematical Identities is "Table of Integrals, Series, and Products" (I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays, 1976), with 4,749 citations. Next come "Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)" (1,767) and "Approximate formulas for some functions of prime numbers" (1,606).

Most cited papers
#PaperReleasedCitations
1 Table of Integrals, Series, and Products I. S. Gradshteyn, I.M. RYZHIK, D. F. Hays · Journal of Lubrication Technology Open access Jul 1976 4,749
2 Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) Milton Abramowitz, Irene A. Stegun, David S. Miller · Journal of Applied Mechanics Mar 1965 1,767
3 Approximate formulas for some functions of prime numbers J. Barkley Rosser, Lowell Schoenfeld · Illinois Journal of Mathematics Open access Mar 1962 1,606
4 HARMONIC POLYLOGARITHMS Ettore Remiddi, J. A. M. Vermaseren · International Journal of Modern Physics A Open access 20 Feb 2000 1,159
5 Probabilistic algorithms for sparse polynomials Richard E. Zippel · Lecture notes in computer science Conference paper 1979 1,134
All 100 most cited papers, with filters and sorting

Where is Advanced Mathematical Identities research done?

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

Largest cities, 2022-now

  1. 1 SeoulSouth Korea 52 works
  2. 2 KharagpurIndia 38 works
  3. 3 NanjingChina 34 works
  4. 4 ParisFrance 34 works
  5. 5 ShanghaiChina 33 works
  6. 6 TokyoJapan 33 works
  7. 7 Xi'anChina 31 works
  8. 8 MoscowRussia 30 works
  9. 9 HangzhouChina 28 works
  10. 10 TianjinChina 27 works

Where it is the local speciality

  1. KharagpurIN · 37.6 works33×
← less than its size predicts1×more →

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, Indian Institute of Technology Kharagpur and Kwangwoon 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%20%40%60%mean 24.6%fractional works in this field (log) →share of work in the world top 10% →Sogang UniversityKwangwoon UniversityPrince Mohammad bin …Indian Institute of …
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
1Sogang UniversitySouth Korea 63.951.2%72.2×12 -3.2%
2Indian Institute of Technology KharagpurIndia 62.013.4%37.5×38 +3132.4%
3Kwangwoon UniversitySouth Korea 61.043.8%102.7×14 -5.8%
4Prince Mohammad bin Fahd UniversitySaudi Arabia 60.521.2%113.5×14 +209.0%
5Suzhou University of Science and TechnologyChina 58.724.7%39.5×17 +668.2%
6Hangzhou Normal UniversityChina 51.826.0%26.5×13 +443.7%
7Aligarh Muslim UniversityIndia 46.026.7%22.1×13 -17.8%
8University of CologneGermany 45.918.3%14.1×12 +27.2%
9Zhoukou Normal UniversityChina 42.79.3%220.7×18 +135.2%
10Akdeniz UniversityTürkiye 40.511.4%39.2×18 -27.8%

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 Advanced Mathematical Identities, country by country

Is Advanced Mathematical Identities research growing?

Output in 2022-2025 was 13% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Advanced Mathematical Identities.

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 Advanced Mathematical Identities as a percentage of every work published that year, 0.0086% in 2024.

still counting0.010%0.020%Advanced Mathematical Identities0.0097% in 202519801990200020102020

Fractional works of Advanced Mathematical Identities 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%Advanced Mathematical Identities10.6% 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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