Metaconjugation and Quadratic Forms
Adriana Cardoso, António Leite, António Machiavelo, Rafael Moreira, Luís Roçadas
Abstract
We present a quaternionic proof that the quadratic form t2+2x2+5y2+10z2 represents all positive integers, and that the form t2+x2+7y2+7z2 represents all natural numbers which are neither equal to 3 · 7 nor equal to 6 · 7, for any ∈ N0. To do this we introduce a technique that may be useful for other purposes, and that we call "metaconjugation".
Create a lesson
Related papers
Explicit equations of Galois subfields of Hermitian function fields with respect to decomposition groups
Liming Ma, Yipeng Wang
Tunnell-type criteria for variants of the congruent number problem
Bo-Hae Im, Minseo Shin
A uniform effective André--Oort result
Guy Fowler
On a conjecture of Browning and Sawin on random hypersurfaces with sign coefficients
Ken Ono, Ashvin Swaminathan
On Multiple Eisenstein Series in Positive Characteristic: Direct Sum Result
Chieh-Yu Chang, Song-Yun Chen, Fei-Jun Huang et al.
Stable Trace Formula for Newton strata of Shimura varieties
Dhruva Kelkar