Concepedia

Height Functions

Height function is a numerical invariant in arithmetic geometry that assigns to each rational point on an algebraic variety a non-negative real number measuring the arithmetic complexity of the point, distinguishing it from other measures by its invariance properties under Galois actions and its role in bounding the number of solutions in Diophantine equations.

141

Publications

6.7K

Citations

208

Authors

150

Institutions

Publications per year

2017–2026

32

Variants

Height Function

Parents

Publications

141

Heights in Diophantine geometry

Choice Reviews Online · 2006 · 495 citations

, , +14

Dimers and amoebae

Richard Kenyon, Andreĭ Okounkov, Scott Sheffield⋆ · Annals of Mathematics · 2006 · 422 citations · Full text

, , +8

Comparison of nonlinear height–diameter functions for major Alberta tree species

Shongming Huang, Stephen J. Titus, Douglas P. Wiens · Canadian Journal of Forest Research · 1992 · 370 citations

, , +17

Positive line bundles on arithmetic varieties

Shou-Wu Zhang · Journal of the American Mathematical Society · 1995 · 243 citations · Full text

, , +10

Critical points and curvature for embedded polyhedra

Thomas Banchoff · Journal of Differential Geometry · 1967 · 224 citations · Full text

, , +14

1–5 of 141

Authors

208

  1. JH
    Joseph H. Silverman

    University of Maryland, College Park, United States

    9 publications · 693 citations

    9

    h-index

  2. MB
    Markus Bussmann

    University of Toronto, Canada

    4 publications · 318 citations

    4

    h-index

  3. SK
    Shu Kawaguchi

    Kyoto University, Japan

    4 publications · 125 citations

    4

    h-index

  4. DM
    David Masser

    University of Basel, Switzerland

    3 publications · 179 citations

    3

    h-index

  5. SS
    Scott Sheffield⋆

    Massachusetts Institute of Technology, United States

    3 publications · 490 citations

    3

    h-index

1–5 of 208

Institutions

150

  1. Brown University

    Providence, United States

    6 h-index

    7 publications

    418 citations

  2. Kyoto University

    Kyoto, Japan

    5 h-index

    5 publications

    198 citations

  3. Courant Institute of Mathematical Sciences

    New York, United States

    4 h-index

    4 publications

    568 citations

  4. Princeton University

    Princeton, United States

    4 h-index

    4 publications

    497 citations

  5. University of Chicago

    Chicago, United States

    4 h-index

    5 publications

    203 citations

  6. Centre National de la Recherche Scientifique

    Paris, France

    4 h-index

    6 publications

    264 citations

  7. University of Cambridge

    Cambridge, United Kingdom

    4 h-index

    4 publications

    80 citations

  8. University of Toronto

    Toronto, Canada

    4 h-index

    9 publications

    687 citations

1–8 of 150

Venues

  1. Duke Mathematical Journal

    DMJ · 7 publications · 423 citations

    7

    h-index

  2. Inventiones mathematicae

    6 publications · 409 citations

    6

    h-index

  3. American Journal of Mathematics

    6 publications · 233 citations

    6

    h-index

  4. Transactions of the American Mathematical Society

    TRAN · 5 publications · 122 citations

    5

    h-index

  5. Journal of Number Theory

    5 publications · 200 citations

    5

    h-index

1–5