Analytic Number Theory Research
Analytic Number Theory Research is a research topic within Algebra and Number Theory. Science Explorer counts 15k research works in it since 1950. 13.6% of them reached the world's top 10% most cited for their field and year.
This cluster of papers focuses on advanced research in prime number theory, L-functions, and their connections to topics such as the Riemann Zeta function, random matrix theory, arithmetic progressions, Vinogradov's mean value theorem, modular forms, and the distribution of primes. It also delves into the exploration of Euler's constant and its implications in number theory.
- Primes
- L-Functions
- Riemann Zeta Function
- Random Matrix Theory
- Arithmetic Progressions
- Vinogradov's Mean Value Theorem
- Modular Forms
- Number Theory
- Distribution of Primes
- Euler's Constant
- Research works
- 15k fractional, since 1950
- In the world top 10%
- 2.1k per year above
- Top-10% rate
- 13.6% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- +3% the tick is no change
Which countries lead Analytic Number Theory Research research?
By volume, China and the United States publish the most (432 and 397 works in 2022–2025).
By volume, 2022–2025
- 1 China 432 works
- 2 United States 397 works
- 3 India 213 works
- 4 Japan 111 works
- 5 France 107 works
- 6 Canada 96 works
- 7 United Kingdom 89 works
- 8 Germany 83 works
- 9 Russia 67 works
- 10 South Korea 57 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 Analytic Number Theory Research research?
By volume in 2022–2025, Shandong University publishes the most Analytic Number Theory Research research, followed by UNSW Sydney and Vilnius University.
By volume, 2022–2025
- 1 Shandong UniversityChina 30 works
- 2 UNSW SydneyAustralia 21 works
- 3 Vilnius UniversityLithuania 20 works
- 4 Université de MontréalCanada 19 works
- 5 Centre National de la Recherche ScientifiqueFrance 18 works
- 6 Northwest UniversityChina 17 works
- 7 University of Illinois Urbana-ChampaignUnited States 15 works
- 8 Suzhou University of Science and TechnologyChina 14 works
- 9 Alfréd Rényi Institute of MathematicsHungary 12 works
- 10 University of OxfordUnited Kingdom 12 works
Who are the leading researchers in Analytic Number Theory Research?
The most-cited researchers publishing on Analytic Number Theory Research include Stephan Ramon Garcia, Steven J. Miller and Terence Tao.
- 1 Stephan Ramon Garcia United States 4k citations
- 2 Steven J. Miller United States 3.8k 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 Analytic Number Theory Research research done?
The largest centres of Analytic Number Theory Research research in 2022–2025 are Jinan (China), Moscow (Russia), Nanjing (China) and Shanghai (China). Among places with at least 20 works in it, it is an unusually large share of all research in Vilnius.
Largest cities, 2022–2025
Where it is the local speciality
- VilniusLT · 20.2 works16×
Location quotient: how much more of its research is in Analytic Number Theory Research than the world average.
Where is the best place to study Analytic Number Theory Research?
Among universities, judged by research, UNSW Sydney, Suzhou University of Science and Technology and Shandong 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 | UNSW SydneyAustralia | 61.1 | 14.8% | 11.5× | 21 | +121.1% |
| 2 | Suzhou University of Science and TechnologyChina | 60.7 | 39.5% | 29.2× | 14 | — |
| 3 | Shandong UniversityChina | 56.7 | 14.9% | 11.6× | 30 | +31.9% |
| 4 | University of CologneGermany | 48.3 | 27.5% | 13.9× | 10 | +8.5% |
| 5 | Université de MontréalCanada | 48.2 | 11.8% | 20.9× | 19 | -11.6% |
| 6 | Vilnius UniversityLithuania | 46.8 | 10.4% | 36.7× | 20 | +9.5% |
| 7 | Sidi Mohamed Ben Abdellah UniversityMorocco | 44.0 | 15.8% | 19.2× | 12 | — |
| 8 | University of WarwickUnited Kingdom | 44.0 | 24.2% | 8.4× | 8 | +92.7% |
| 9 | Shanghai UniversityChina | 43.2 | 56.3% | 5.4× | 9 | +7.9% |
| 10 | Shandong Normal UniversityChina | 43.1 | 16.2% | 19.8× | 11 | +62.2% |
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 Analytic Number Theory Research research growing?
Output in 2018–2022 was 3% higher than in 2013–2017, peaking in 2025. The fastest-growing topics are Analytic Number Theory Research.
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.