Concepedia

Sum-product Phenomena

Sum–Product Phenomena is a theoretical framework in additive combinatorics that asserts, for a finite set of numbers, either the sumset or the product set must be significantly larger than the original set, reflecting the incompatibility of additive and multiplicative structure.

58

Publications

3.4K

Citations

79

Authors

71

Institutions

Publications per year

2017–2026

7

Variants

Sum-product Phenomenon

Parents

Publications

58

Second Memoir on the Expansion of certain Infinite Products

L. J. Rogers · Proceedings of the London Mathematical Society · 1893 · 453 citations

, , +7

A sum-product estimate in finite fields, and applications

Jean Bourgain, Nets Hawk Katz, Terence Tao · Geometric and Functional Analysis · 2004 · 377 citations

, , +7

MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS

Jean Bourgain · International Journal of Number Theory · 2005 · 261 citations

, , +8

Space–time analysis using a general product–sum model

Sandra De Iaco, Donald E. Myers, D. Posa · Statistics & Probability Letters · 2001 · 189 citations

, , +5

A theorem in additive number theory

Roger Crocker · Colloquium Mathematicum · 1969 · 175 citations · Full text

, , +9

1–5 of 58

Authors

79

  1. ID
    Ilya D. Shkredov

    Steklov Mathematical Institute, Russia

    6 publications · 150 citations

    6

    h-index

  2. MR
    Misha Rudnev

    University of Bristol, United Kingdom

    5 publications · 123 citations

    5

    h-index

  3. CS
    Carsten Schneider

    Johannes Kepler University of Linz, Austria

    3 publications · 157 citations

    3

    h-index

  4. PE
    P. Erdös

    Hungarian Academy of Sciences, Hungary

    3 publications · 144 citations

    3

    h-index

  5. TT
    Terence Tao

    University of California, Los Angeles, United States

    3 publications · 438 citations

    3

    h-index

1–5 of 79

Institutions

71

  1. Steklov Mathematical Institute

    Moscow, Russia

    5 h-index

    6 publications

    163 citations

  2. Johannes Kepler University of Linz

    Linz, Austria

    3 h-index

    3 publications

    157 citations

  3. University of Bristol

    Bristol, United Kingdom

    3 h-index

    4 publications

    146 citations

  4. Institute for Advanced Study

    Princeton, United States

    3 h-index

    4 publications

    982 citations

  5. Centre National de la Recherche Scientifique

    Paris, France

    3 h-index

    3 publications

    93 citations

  6. University of Pennsylvania

    Philadelphia, United States

    2 h-index

    2 publications

    106 citations

  7. Laboratoire de Mathématiques Blaise Pascal

    Aubière, France

    2 h-index

    2 publications

    71 citations

  8. Moscow Institute of Physics and Technology

    Dolgoprudnyy, Russia

    2 h-index

    2 publications

    67 citations

1–8 of 71

Venues

  1. Advances in Mathematics

    3 publications · 108 citations

    3

    h-index

  2. Animal Learning & Behavior

    2 publications · 106 citations

    2

    h-index

  3. Acta Arithmetica

    2 publications · 82 citations

    2

    h-index

  4. Journal of Symbolic Computation

    2 publications · 132 citations

    2

    h-index

  5. European Journal of Combinatorics

    2 publications · 120 citations

    2

    h-index

1–5