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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. 10.2% 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%
1.6k
per year above
Top-10% rate
10.2%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+19%
the tick is no change
Largest producer
China
26% of the 10 largest, 2022-now
Analytic Number Theory Research

Which countries lead Analytic Number Theory Research research?

By volume, China and the United States publish the most (508 and 482 works in 2022-now).

By volume, 2022-now

  1. 1 China 508 works
  2. 2 United States 482 works
  3. 3 India 249 works
  4. 4 Japan 126 works
  5. 5 France 121 works
  6. 6 Canada 108 works
  7. 7 United Kingdom 101 works
  8. 8 Germany 96 works
  9. 9 Russia 75 works
  10. 10 South Korea 62 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: 26.3%United States: 25.0%India: 12.9%Japan: 6.5%6 others listed: 29.2%26%largest
China508 · 26.3%United States482 · 25.0%India249 · 12.9%Japan126 · 6.5%6 others listed563 · 29.2%

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

Which institutions lead Analytic Number Theory Research research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Analytic Number Theory Research research, followed by Shandong University and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 61 works
  2. 2 Shandong UniversityChina 32 works
  3. 3 Russian Academy of SciencesRussia 28 works
  4. 4 UNSW SydneyAustralia 27 works
  5. 5 Vilnius UniversityLithuania 22 works
  6. 6 Université de MontréalCanada 20 works
  7. 7 Northwest UniversityChina 18 works
  8. 8 University of Illinois Urbana-ChampaignUnited States 17 works
  9. 9 Suzhou University of Science and TechnologyChina 14 works
  10. 10 Shandong Normal UniversityChina 14 works

Who are the leading researchers in Analytic Number Theory Research?

The most-cited researchers publishing on Analytic Number Theory Research include R. W. L. Jones.

  1. 1 R. W. L. Jones United Kingdom 189k 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 Analytic Number Theory Research?

The most cited paper in Analytic Number Theory Research is "Factoring polynomials with rational coefficients" (A. K. Lenstra, Hendrik W. Lenstra, László Lovász, 1982), with 4,058 citations. Next come "Algebraic number theory" (2,174) and "Approximate formulas for some functions of prime numbers" (1,606).

Most cited papers
#PaperReleasedCitations
1 Factoring polynomials with rational coefficients A. K. Lenstra, Hendrik W. Lenstra, László Lovász · Mathematische Annalen Open access Dec 1982 4,058
2 Algebraic number theory Kazuya Katô, Nobushige Kurokawa, Takeshi Saito · Translations of mathematical monographs Book chapter 22 Nov 1999 2,174
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 A Probabilistic Proof of an Asymptotic Formula for the Number of Labelled Regular Graphs Béla Bollobás · European Journal of Combinatorics Open access Dec 1980 1,208
5 An approximation of partial sums of independent RV's, and the sample DF. II J. Koml�s, Péter Major, G. Tusn�dy · Probability Theory and Related Fields Open access 1976 1,025
All 100 most cited papers, with filters and sorting

Where is Analytic Number Theory Research research done?

The largest centres of Analytic Number Theory Research research in 2022-now are Jinan (China), Moscow (Russia), Beijing (China) and Nanjing (China). Among places with at least 20 works in it, it is an unusually large share of all research in Vilnius.

Largest cities, 2022-now

  1. 1 JinanChina 51 works
  2. 2 MoscowRussia 47 works
  3. 3 BeijingChina 43 works
  4. 4 NanjingChina 41 works
  5. 5 TokyoJapan 41 works
  6. 6 ParisFrance 40 works
  7. 7 ShanghaiChina 39 works
  8. 8 Xi'anChina 37 works
  9. 9 SeoulSouth Korea 30 works
  10. 10 MontrealCanada 26 works

Where it is the local speciality

  1. VilniusLT · 22.8 works15×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Analytic Number Theory Research than the world average.

See Analytic Number Theory Research on the map

Where is the best place to study Analytic Number Theory Research?

Among universities, judged by research, Suzhou University of Science and Technology, UNSW Sydney 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.

0%20%40%mean 20.27%fractional works in this field (log) →share of work in the world top 10% →Shanghai UniversitySuzhou University of…UNSW SydneyShandong University
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
1Suzhou University of Science and TechnologyChina 69.630.4%29.5×14 +580.4%
2UNSW SydneyAustralia 64.913.2%12.9×27 +35.4%
3Shandong UniversityChina 62.512.4%10.6×32 +32.6%
4Shanghai UniversityChina 60.341.1%5.4×9 +90.3%
5Université de MontréalCanada 57.610.3%15.6×20 +446.2%
6University of CologneGermany 56.528.0%10.7×11 +67.9%
7University of WarwickUnited Kingdom 54.221.9%9.7×10 +39.4%
8Sidi Mohamed Ben Abdellah UniversityMorocco 50.318.6%19.3×12 +414.8%
9ETH ZurichSwitzerland 50.114.0%6.4×10 +34.9%
10University of OxfordUnited Kingdom 48.912.8%4.1×13 +35.5%

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 Analytic Number Theory Research, country by country

Is Analytic Number Theory Research research growing?

Output in 2022-2025 was 19% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Analytic Number Theory Research.

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 Analytic Number Theory Research as a percentage of every work published that year, 0.010% in 2024.

still counting0.010%0.020%0.030%Analytic Number Theory Research0.011% in 202519801990200020102020

Fractional works of Analytic Number Theory Research 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%Analytic Number Theory Research11.4% 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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