Upper Bounds for the Number of Solutions of a Diophantine Equation
نویسندگان
چکیده
We give upper bound estimates for the number of solutions of a certain diophantine equation. Our results can be applied to obtain new lower bound estimates for the L1-norm of certain exponential sums.
منابع مشابه
Upper bounds on the solutions to n = p+m^2
ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...
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