Concepedia

Waring's Problem

Waring's Problem is a foundational question in additive number theory that seeks to determine, for each positive integer $ k $, the smallest integer $ g(k) $ such that every natural number can be expressed as a sum of at most $ g(k) $ $ k $-th powers of non-negative integers.

111

Publications

3.4K

Citations

104

Authors

67

Institutions

Publications per year

2017–2026

6

Parents

Publications

111

Cyclotomy, Higher Congruences, and Waring's Problem

L. E. Dickson · American Journal of Mathematics · 1935 · 158 citations

, , +5

Cyclotomy, Higher Congruences, and Waring's Problem II

L. E. Dickson · American Journal of Mathematics · 1935 · 133 citations

, , +8

The solution to the Waring problem for monomials and the sum of coprime monomials

Enrico Carlini, Maria Virginia Catalisano, Anthony V. Geramita · Journal of Algebra · 2012 · 125 citations

, , +9

Vinogradov's mean value theorem via efficient congruencing

Trevor D. Wooley · Annals of Mathematics · 2012 · 112 citations · Full text

, , +4

Word maps and Waring type problems

Michael Larsen, Aner Shalev · Journal of the American Mathematical Society · 2008 · 91 citations · Full text

, , +15

1–5 of 111

Authors

104

  1. TD
    Trevor D. Wooley

    University of Michigan, United States

    14 publications · 523 citations

    13

    h-index

  2. RC
    R. C. Vaughan

    Imperial College London, United Kingdom

    9 publications · 361 citations

    9

    h-index

  3. JB
    Jörg Brüdern

    University of Stuttgart, Germany

    8 publications · 136 citations

    8

    h-index

  4. AS
    Aner Shalev

    Hebrew University of Jerusalem, Israel

    4 publications · 226 citations

    4

    h-index

  5. MV
    Maria Virginia Catalisano

    University of Genoa, Italy

    3 publications · 169 citations

    3

    h-index

1–5 of 104

Institutions

67

  1. University of Michigan

    Ann Arbor, United States

    9 h-index

    10 publications

    347 citations

  2. Imperial College London

    London, United Kingdom

    5 h-index

    5 publications

    173 citations

  3. University of Bristol

    Bristol, United Kingdom

    4 h-index

    4 publications

    167 citations

  4. University of Stuttgart

    Stuttgart, Germany

    4 h-index

    4 publications

    79 citations

  5. Iwate University

    Morioka, Japan

    4 h-index

    4 publications

    130 citations

  6. Indiana University Bloomington

    Bloomington, United States

    3 h-index

    3 publications

    196 citations

  7. Hebrew University of Jerusalem

    Jerusalem, Israel

    3 h-index

    3 publications

    196 citations

  8. Shandong University

    Jinan, China

    3 h-index

    4 publications

    68 citations

1–8 of 67

Venues

  1. Acta Arithmetica

    13 publications · 223 citations

    11

    h-index

  2. Proceedings of the London Mathematical Society

    8 publications · 287 citations

    8

    h-index

  3. 7

    h-index

  4. Journal of the London Mathematical Society

    6 publications · 126 citations

    6

    h-index

  5. The Quarterly Journal of Mathematics

    5 publications · 90 citations

    5

    h-index

1–5