Concepedia

Counting Rational Points

Counting Rational Points is a foundational problem in Computational Number Theory that involves determining the number of solutions to polynomial equations over a given number field, typically focusing on solutions that are rational or lie in a specified algebraic extension, thereby quantifying the arithmetic structure of algebraic varieties.

335

Publications

14.1K

Citations

391

Authors

265

Institutions

Publications per year

2017–2026

26

Parents

Publications

335

Exponential Sums and Lattice Points III

M. N. Huxley · Proceedings of the London Mathematical Society · 2003 · 484 citations

, , +10

Rational points of abelian varieties with values in towers of number fields

Barry Mazur · Inventiones mathematicae · 1972 · 443 citations

, , +10

Number of Points of Varieties in Finite Fields

Serge Lang · American Journal of Mathematics · 1954 · 431 citations

, , +9

Rational points of bounded height on Fano varieties

Jens Frankē, Yuri I. Manin, Yuri Tschinkel · Inventiones mathematicae · 1989 · 367 citations

, , +5

The number of integral points on arcs and ovals

Enrico Bombieri, Jonathan Pila · Duke Mathematical Journal · 1989 · 292 citations

, , +7

1–5 of 335

Authors

391

  1. DR
    D. R. Heath‐Brown

    Northeast Catholic College, United States

    9 publications · 504 citations

    9

    h-index

  2. TD
    T. D. Browning

    University of Bristol, United Kingdom

    8 publications · 202 citations

    8

    h-index

  3. JH
    Joseph H. Silverman

    University of Maryland, College Park, United States

    7 publications · 278 citations

    7

    h-index

  4. JP
    Jonathan Pila

    University of Bristol, United Kingdom

    5 publications · 467 citations

    5

    h-index

  5. PG
    Pierrick Gaudry

    Centre National de la Recherche Scientifique, France

    5 publications · 185 citations

    5

    h-index

1–5 of 391

Institutions

265

  1. University of Bristol

    Bristol, United Kingdom

    11 h-index

    12 publications

    457 citations

  2. Massachusetts Institute of Technology

    Cambridge, United States

    10 h-index

    10 publications

    386 citations

  3. Brown University

    Providence, United States

    8 h-index

    8 publications

    242 citations

  4. Centre National de la Recherche Scientifique

    Paris, France

    7 h-index

    8 publications

    228 citations

  5. University of Duisburg-Essen

    Essen, Germany

    7 h-index

    7 publications

    404 citations

  6. University of Michigan

    Ann Arbor, United States

    6 h-index

    10 publications

    387 citations

  7. KU Leuven

    Leuven, Belgium

    6 h-index

    9 publications

    491 citations

  8. University of California, Berkeley

    Berkeley, United States

    6 h-index

    6 publications

    462 citations

1–8 of 265

Venues

  1. Duke Mathematical Journal

    DMJ · 15 publications · 1.1K citations

    14

    h-index

  2. Algebra & Number Theory

    ANT · 12 publications · 434 citations

    12

    h-index

  3. Journal of Number Theory

    12 publications · 336 citations

    12

    h-index

  4. ArXiv.org

    Repository · 12 publications · 554 citations

    11

    h-index

  5. Proceedings of the London Mathematical Society

    9 publications · 912 citations

    9

    h-index

1–5