M. Pandey

activity

20162026

most citedSecurity of Healthcare Data Using Blockchains: A Survey

2 citations · 2 across the 3 of their papers we have counts for

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5 papers · 1 filter

math.NT2021

On the distribution of additive twists of the divisor function and Hecke eigenvalues

Mayank Pandey

We obtain asymptotics with a power saving error term for $\int_{0}^{1} ∣ \sum_{n \leq X} d (n) e (n α) ∣^{s} d α$ for $s < 2$ , where $d (n) = \sum_{d ∣ n} 1$ is the divisor function. We also obtain…

math.NT2019

Moment estimates for the exponential sum with higher divisor functions

Mayank Pandey

We obtain asymptotic for the quantity $\int_{0}^{1} \sum_{n \leq X} τ_{k} (n) e (n α) d α$ where $τ_{k} (n) = \sum_{d_{1} \dots d_{k} = n} 1$ . This follows from a quick application of the cir…

math.NT2019

On the mean value of the magnitude of an exponential sum involving the divisor function

Mayank Pandey

We obtain an asymptotic formula for the L^1 norm of the exponential sum $M (α) = \sum_{n \leq X} τ (n) e (n α)$ where $τ (n) = \sum_{d ∣ n} 1$ is the divisor function. In particular, we show…

math.NT2018

Moments of an exponential sum related to the divisor function

Mayank Pandey

We use the circle method to obtain tight bounds on the $L^{p}$ norm of an exponential sum involving the divisor function for $p > 2$ .

math.NT2016

On the Waring-Goldbach Problem for tenth powers

Mayank Pandey

Using sharper Weyl sum estimates, we show that $H (10) \leq 105$ , improving upon the previous bound of $107$ .