Canonical Ternary Quadratic Forms: Linear Algebraic Approach

EasyChair Preprint 15935

Abstract

               In  this  research  paper,  it  is  reasoned  that  “canonical”/interesting  ternary  quadratic 

              forms  ( in  the  spirit  of  Ramanujan ternary  quadratic  form)  fall  in  2  distinct  quadratic 

              form  classes.   Two interesting  theorems  are  proved  which  show  that  when  the 

              eigenvalues  of   symmetric  matrices  associated  with  the  canonical  ternary  forms  are 

              integers,  the ternary  quadratic  form  can  never  equal  the  square  of   an  integer. 

              Alongwith  Fermat’s   last  number  Theorem,  these   Theorems   provide  new  results on

              representation  of  integers  using  higher   degree  ternary  forms

Keyphrases: Higher Degree Forms, Quadratic Surds, Symmetric matrices, Ternary Quadratic Form, eigenvalues

@booklet{EasyChair:15935,
  author    = {Rama Murthy Garimella},
  title     = {Canonical  Ternary  Quadratic  Forms: Linear Algebraic  Approach},
  howpublished = {EasyChair Preprint 15935},
  year      = {EasyChair, 2025}}