Manoj Verma

collaborators

3 papers

math.NT2014

On a form of degree $d$ in $2 d + 1$ variables ( $d \geq 4$ )

Manoj Verma

For $k \geq 2$ , we derive an asymptotic formula for the number of zeros of the forms $\prod_{i = 1}^{k} (x_{2 i - 1}^{2} + x_{2 i}^{2}) + \prod_{i = 1}^{k} (x_{2 k + 2 i - 1}^{2} + x_{2 k + 2 i}^{2}) - x_{4 k + 1}^{2 k}$ …

math.NT2014

Proof of Bertrand's Postulate for $n \geq 6$

Manoj Verma

We add a few ideas to Erdős's proof of Bertrand's Postulate to produce one using a little calculus but requiring direct check only for $n \leq 5$ and one without using calculus and…

math.NT2013

Representation of integers by a family of cubic forms in seven variables II

Manoj Verma

In an earlier paper [4], we derived asymptotic formulas for the number of representations of zero and of large positive integers by the cubic forms in seven variables which can be…

On a form of degree d in 2d+1 variables (d≥4)

Proof of Bertrand's Postulate for n≥6

Representation of integers by a family of cubic forms in seven variables II

On a form of degree $d$ in $2 d + 1$ variables ( $d \geq 4$ )

Proof of Bertrand's Postulate for $n \geq 6$