Anuradha S. Garge

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20122026

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math.NT2026

Integral quadratic forms over a ring of $p$ -adic integers

Mrunal Hardikar, Anuradha S. Garge

Jungin Lee in 2018 proved a necessary and sufficient condition that an integral quadratic form $\sum_{i = 1}^{m} a_{i} X_{i}^{2}$ is universal over $M_{2} (Z)$ . For a positive integer…

math.NT2020

Trace and discriminant criteria for a matrix to be a sum of sixth and eighth powers of matrices

Rakesh Barai, Anuradha S. Garge

In this paper, we shall be considering the Waring's problem for matrices. One version of the problem involves writing an $n \times n$ matrix over a commutative ring $R$ with unity…

math.NT2020

Representation of two by two matrices over perfect fields by a diagonal quadratic form

Murtuza Nullwala, Anuradha S. Garge

Let F be a perfect field. Then the diagonal quadratic form $a_{i} X_{i}^{2}$ over $F$ is universal over $M_{2} (F)$ if and only if atleast two of the $a_{i}$ are non-zero.

Integral quadratic forms over a ring of p-adic integers

Trace and discriminant criteria for a matrix to be a sum of sixth and eighth powers of matrices

Representation of two by two matrices over perfect fields by a diagonal quadratic form

Integral quadratic forms over a ring of $p$ -adic integers