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ON THE SUM OF HIGHER DIVISOR FUNCTION WITH ALMOST EQUAL PRIME VARIABLES
Keywords:
Higher divisor function, prime variables, circle methodDOI:
https://doi.org/10.17654/0972555525033Abstract
Let $k, r \geq 2$ be integers, and let $\tau_k(n)$ denote the $k$ th divisor function. Let $\ell_r, \theta_r$ be defined in Theorem 1.1. Assuming that the integer $\ell>\ell_r$, we consider $Y=X^{\theta_r+\varepsilon}$ as it approaches infinity. We apply the Hardy-Littlewood circle method to derive an asymptotic formula for the sum
Received: June 20, 2025
Revised: July 15, 2025
Accepted: July 25, 2025
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