| Autor: |
Nullwala, Murtuza, Garge, Anuradha S. |
| Zdroj: |
Indian Journal of Pure & Applied Mathematics; Mar2024, Vol. 55 Issue 1, p54-68, 15p |
| Abstrakt: |
In 2018, Jungin Lee [5] gave a necessary and sufficient condition for a diagonal quadratic form ∑ i = 1 m a i X i 2 where a i ∈ Z for all i, 1 ≤ i ≤ m for representing all 2 × 2 matrices over Z . In this paper, we will consider the imaginary quadratic field Q (- 7) . Its ring of integers O is a principal ideal domain. Q (- 7) is the only imaginary quadratic field such that O is a principal ideal domain and 2 is a product of two distinct primes in O (upto units). With O as above, in this paper we give a necessary and sufficient condition for a diagonal quadratic form a 1 X 1 2 + a 2 X 2 2 + a 3 X 3 2 where a 1 , a 2 , a 3 ∈ O to represent all 2 × 2 matrices over O . [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
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