1986/11/01 by W. D. Brownawell, W. Dale Brownawell, David Masser +1 · 1 citation
Mathematics · Medicine · #Algebraic Geometry and Number Theory #Combinatorics #Discrete valuation #Field (mathematics) #Function (biology) #Function field #Genus #Magnolia and Illicium research #Mathematical analysis #Mathematics #Meromorphic and Entire Functions #Order (exchange) #Projective space #Projective test #Pure mathematics #Rational function #Valuation (finance) #Zero (linguistics) #Zoology
paper · doi:10.1017/s0305004100066184
openalex publication_date 1986/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
Let k be a field of zero characteristic, and let F be a function field over k of genus g . We normalize each valuation v on F so that its order group consists of all rational integers, and for elements u 1 , …, u n of F , not all zero, we define the (projective) height as The sum formula on F shows that this is really a height on the projective space .