Concepedia

Modular Arithmetic

Modular Arithmetic is a branch of number theory that studies the properties and operations of integers under a congruence relation defined by a fixed positive integer modulus, distinguishing it from other arithmetic systems by its cyclic structure and equivalence class partitioning of the integers.

2.6K

Publications

103.4K

Citations

2.9K

Authors

1.1K

Institutions

Publications per year

2017–2026

242

Parents

Children

Publications

2.6K

Modular multiplication without trial division

Peter L. Montgomery · Mathematics of Computation · 1985 · 2.4K citations

, , +9

Modular Elliptic Curves and Fermat's Last Theorem

Andrew Wiles · Annals of Mathematics · 1995 · 2.1K citations

, , +11

Speeding the Pollard and elliptic curve methods of factorization

Peter L. Montgomery · Mathematics of Computation · 1987 · 1.2K citations

, , +16

Modular Multiplication Without Trial Division

Peter L. Montgomery · Mathematics of Computation · 1985 · 1.1K citations · Full text

, , +9

On Modular Forms of Half Integral Weight

Goro Shimura · Annals of Mathematics · 1973 · 989 citations

, , +12

1–5 of 2.6K

Authors

2.9K

  1. KO
    Ken Ono

    University of Wisconsin–Madison, United States

    24 publications · 1.6K citations

    19

    h-index

  2. IE
    Igor E. Shparlinski

    Macquarie University, Australia

    21 publications · 475 citations

    13

    h-index

  3. ÇK
    Çetin Kaya Koç

    Oregon State University, United States

    12 publications · 956 citations

    12

    h-index

  4. JB
    Jean-Claude Bajard

    Centre National de la Recherche Scientifique, France

    12 publications · 504 citations

    12

    h-index

  5. LS
    Leonel Sousa

    Instituto de Engenharia de Sistemas e Computadores Investigação e Desenvolvimento, Portugal

    11 publications · 342 citations

    11

    h-index

1–5 of 2.9K

Institutions

1.1K

  1. Centre National de la Recherche Scientifique

    Paris, France

    27 h-index

    68 publications

    3.4K citations

  2. Harvard University

    Cambridge, United States

    21 h-index

    35 publications

    5.7K citations

  3. Pennsylvania State University

    State College, United States

    19 h-index

    31 publications

    999 citations

  4. Institute for Advanced Study

    Princeton, United States

    19 h-index

    28 publications

    1.7K citations

  5. University of Cambridge

    Cambridge, United Kingdom

    18 h-index

    23 publications

    915 citations

  6. University of Wisconsin–Madison

    Madison, United States

    18 h-index

    34 publications

    2.4K citations

  7. Max Planck Institute for Mathematics

    Bonn, Germany

    17 h-index

    30 publications

    2.1K citations

  8. Princeton University

    Princeton, United States

    17 h-index

    23 publications

    1.3K citations

1–8 of 1.1K

Venues

  1. Inventiones mathematicae

    63 publications · 5.3K citations

    39

    h-index

  2. Journal of Number Theory

    166 publications · 4.2K citations

    33

    h-index

  3. Annals of Mathematics

    39 publications · 7.5K citations

    31

    h-index

  4. Mathematics of Computation

    MCOM · 110 publications · 7.6K citations

    29

    h-index

  5. Acta Arithmetica

    108 publications · 2.7K citations

    28

    h-index

1–5