Topic · Analytic Number Theory Research
Most cited papers in Analytic Number Theory Research
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).
Showing 50 of 100 papers. Every paper with more than 255 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | Factoring polynomials with rational coefficients A. K. Lenstra, Hendrik W. Lenstra, László Lovász · Mathematische Annalen | Dec 1982 | 4,058 |
| 2 | Algebraic number theory Kazuya Katô, Nobushige Kurokawa, Takeshi Saito · Translations of mathematical monographs | 22 Nov 1999 | 2,174 |
| 3 | Approximate formulas for some functions of prime numbers J. Barkley Rosser, Lowell Schoenfeld · Illinois Journal of Mathematics | 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 | 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 | 1976 | 1,025 |
| 6 | PRIMES is in P Manindra Agrawal, Neeraj Kayal, Nitin Saxena · Annals of Mathematics | Sep 2004 | 936 |
| 7 | The Riemann Zeta Function Anatolij A. Karatsuba, Melvyn B. Nathanson | 31 Dec 1992 | 905 |
| 8 | The primes contain arbitrarily long arithmetic progressions Benjamin Green, Terence Tao · Annals of Mathematics | Mar 2008 | 832 |
| 9 | An approximation of partial sums of independent RV'-s, and the sample DF. I J. Koml�s, Péter Major, G. Tusn�dy · Probability Theory and Related Fields | 1975 | 801 |
| 10 | On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises Christophe Breuil, Brian Conrad, Fred Diamond et al. · Journal of the American Mathematical Society | 15 May 2001 | 791 |
| 11 | A new proof of Szemerédi's theorem W. T. Gowers · Geometric and Functional Analysis | 15 Aug 2001 | 728 |
| 12 | On the normal concentration of divisors, 2 Helmut Maier, Gérald Tenenbaum · Mathematical Proceedings of the Cambridge Philosophical Society | 6 Jul 2009 | 697 |
| 13 | Hecke operators on ?0(m) A. O. L. Atkin, Joseph Lehner · Mathematische Annalen | Jun 1970 | 696 |
| 14 | Multiplicative Number Theory I: Classical Theory Hugh L. Montgomery, Robert Charles Vaughan · CERN Document Server (European Organization for Nuclear Research) | 2006 | 678 |
| 15 | Ten Lectures on the Interface between Analytic Number Theory and Harmonic Analysis Hugh L. Montgomery · Regional conference series in mathematics | 11 Oct 1994 | 673 |
| 16 | Values of Zeta Functions and Their Applications Don Bernard Zagier · Birkhäuser Basel eBooks | 1994 | 659 |
| 17 | On Certain Sets of Integers K. F. Roth · Journal of the London Mathematical Society | 1953 | 623 |
| 18 | L-Functions and Tamagawa Numbers of Motives Spencer Janney Bloch, Kazuya Katô · Modern Birkhäuser classics | 2007 | 616 |
| 19 | Longest Increasing and Decreasing Subsequences C. Schensted · Canadian Journal of Mathematics | 1961 | 595 |
| 20 | Ramanujan's Notebooks Bruce C. Berndt · Mathematics Magazine | May 1978 | 587 |
| 21 | Zeros of principal L-functions and random matrix theory Zeév Rudnick, Peter Sarnak · Duke Mathematical Journal | 1996 | 585 |
| 22 | 𝑞-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics and Computer Algebra George E. Andrews · Regional conference series in mathematics | 31 Dec 1986 | 532 |
| 23 | Low-discrepancy and low-dispersion sequences Harald Niederreiter · Journal of Number Theory | Sep 1988 | 496 |
| 24 | Ramanujan's Lost Notebook: Part II George E. Andrews, Bruce C. Berndt · DIAL (Catholic University of Leuven) | 2009 | 494 |
| 25 | Exponential Sums and Lattice Points III M. N. Huxley · Proceedings of the London Mathematical Society | 23 Oct 2003 | 490 |
| 26 | Nonconventional ergodic averages and nilmanifolds Bernard Host, Bryna Kra · Annals of Mathematics | 2005 | 485 |
| 27 | Bounded gaps between primes Zhang Yitang · Annals of Mathematics | 20 Feb 2014 | 468 |
| 28 | Numerical evaluation of multiple polylogarithms Jens Vollinga, Stefan Weinzierl · Computer Physics Communications | 12 Mar 2005 | 464 |
| 29 | Liaison des vari�t�s alg�briques. I Christian Peskine, Lucien Szpiro · Inventiones mathematicae | Dec 1974 | 457 |
| 30 | Cascades of sigma factors Richard M. Losick, Janice G. Pero · Cell | Sep 1981 | 447 |
| 31 | Rational points of abelian varieties with values in towers of number fields Barry Mazur · Inventiones mathematicae | Dec 1972 | 446 |
| 32 | Zeroes of zeta functions and symmetry Nicholas Katz, Peter Sarnak · Bulletin of the American Mathematical Society | 1999 | 442 |
| 33 | Analyticity of sets associated to Lelong numbers and the extension of closed positive currents Yum-Tong Siu · Inventiones mathematicae | Mar 1974 | 437 |
| 34 | The Difference Between Consecutive Primes, II Roger C. Baker, Güneş Harman, J. Pintz · Proceedings of the London Mathematical Society | Nov 2001 | 429 |
| 35 | Sums involving the values at negative integers of L-functions of quadratic characters Henri Cohen · Mathematische Annalen | Oct 1975 | 429 |
| 36 | Introduction Richard R. Hall · Cambridge University Press eBooks | 10 Oct 1996 | 422 |
| 37 | The Number of Partitions of a Set Gian‐Carlo Rota · American Mathematical Monthly | May 1964 | 415 |
| 38 | Integral moments of L-functions J. Brian Conrey, D. W. Farmer, Jonathan P. Keating et al. · Proceedings of the London Mathematical Society | 22 Jun 2005 | 412 |
| 39 | Fuglede’s conjecture is false in 5 and higher dimensions Terence Tao · Mathematical Research Letters | 2004 | 411 |
| 40 | A Hecke Algebra of (Z/rZ)Sn and Construction of Its Irreducible Representations S. Ariki, Kazuhiko Koike · Advances in Mathematics | Jul 1994 | 407 |
| 41 | Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals Erik Panzer · Computer Physics Communications | 30 Oct 2014 | 401 |
| 42 | Low lying zeros of families of L -functions Henryk Iwaniec, Wenzhi Luo, Peter Sarnak · Publications mathématiques de l IHÉS | 7 Dec 2000 | 399 |
| 43 | Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers Yann Bugeaud, Maurice Mignotte, Samir Siksek · Annals of Mathematics | May 2006 | 390 |
| 44 | Hyperbolic distribution problems and half-integral weight Maass forms William Duke · Inventiones mathematicae | Feb 1988 | 387 |
| 45 | Dyson’s crank of a partition George E. Andrews, Frank G. Garvan · Bulletin of the American Mathematical Society | 1988 | 387 |
| 46 | Linear equations in primes Ben Green, Terence Tao · Annals of Mathematics | 25 Apr 2010 | 386 |
| 47 | A sum-product estimate in finite fields, and applications Jean Bourgain, Nets Hawk Katz, Terence Tao · Geometric and Functional Analysis | Feb 2004 | 379 |
| 48 | Hilbert's Tenth Problem is Unsolvable Martin D. Davis · American Mathematical Monthly | Mar 1973 | 376 |
| 49 | Cryptographic Hash Functions from Expander Graphs Denis Xavier Charles, Kristin Lauter, Eyal Z. Goren · Journal of Cryptology | 14 Sep 2007 | 376 |
| 50 | Special values of multiple polylogarithms Jonathan Michael Borwein, David M. Bradley, David Broadhurst et al. · Transactions of the American Mathematical Society | 11 Oct 2000 | 372 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.