Concepedia

Ramanujan Sum

Ramanujan Sum is an arithmetic function that, for a given integer \( n \) and a positive integer \( q \), is defined as the sum of the \( n \)-th powers of the primitive \( q \)-th roots of unity, distinguishing it from other trigonometric or number-theoretic sums by its explicit connection to multiplicative characters and its role in the expansion of arithmetic functions in terms of periodic components.

600

Publications

23.2K

Citations

590

Authors

369

Institutions

Publications per year

2017–2026

60

Variants

Ramanujan SumsRamanujan's Sum

Parents

Publications

600

Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities

George E. Andrews, R. J. Baxter, Peter J. Forrester · Journal of Statistical Physics · 1984 · 881 citations

, , +7

Mock Theta Functions

Sander Zwegers · ArXiv.org · 2008 · 433 citations · Full text

, , +13

Further Identities of the Rogers-Ramanujan Type

Louise Slater · Proceedings of the London Mathematical Society · 1952 · 387 citations

, , +6

Number theory in the spirit of Ramanujan

Choice Reviews Online · 2007 · 344 citations

, , +8

Existence and Explicit Constructions of q + 1 Regular Ramanujan Graphs for Every Prime Power q

Moshe Morgenstern · Journal of Combinatorial Theory Series B · 1994 · 310 citations

, , +4

1–5 of 600

Authors

590

  1. GE
    George E. Andrews

    Pennsylvania State University, United States

    26 publications · 2.5K citations

    22

    h-index

  2. BC
    Bruce C. Berndt

    University of Illinois Urbana-Champaign, United States

    35 publications · 1.3K citations

    21

    h-index

  3. HH
    Heng Huat Chan

    National University of Singapore, Singapore

    17 publications · 587 citations

    13

    h-index

  4. JG
    Jesús Guillera

    Zaragoza Logistics Center, Spain

    10 publications · 350 citations

    10

    h-index

  5. MD
    Michael D. Hirschhorn

    UNSW Sydney, Australia

    10 publications · 263 citations

    10

    h-index

1–5 of 590

Institutions

369

  1. Pennsylvania State University

    State College, United States

    25 h-index

    42 publications

    3.2K citations

  2. University of Illinois Urbana-Champaign

    Urbana, United States

    20 h-index

    43 publications

    1.4K citations

  3. Centre National de la Recherche Scientifique

    Paris, France

    14 h-index

    27 publications

    729 citations

  4. University of Wisconsin–Madison

    Madison, United States

    13 h-index

    19 publications

    1.2K citations

  5. National University of Singapore

    Singapore, Singapore

    13 h-index

    21 publications

    691 citations

  6. University of Florida

    Gainesville, United States

    11 h-index

    12 publications

    452 citations

  7. UNSW Sydney

    Sydney, Australia

    10 h-index

    10 publications

    263 citations

  8. Massey University

    Palmerston North, New Zealand

    9 h-index

    9 publications

    205 citations

1–8 of 369

Venues

  1. The Ramanujan Journal

    55 publications · 1.4K citations

    21

    h-index

  2. Transactions of the American Mathematical Society

    TRAN · 20 publications · 1K citations

    17

    h-index

  3. Journal of Number Theory

    27 publications · 756 citations

    17

    h-index

  4. Advances in Mathematics

    19 publications · 1K citations

    17

    h-index

  5. 16

    h-index

1–5