Consider the divisor sum (Formula presented.) for integers b and c. We improve the explicit upper bound of this average divisor sum in certain cases, and as an application, we give an improvement in the maximal possible number of (Formula presented.)-quadruples. The new tool is a numerically explicit Pólya–Vinogradov inequality, which has not been formulated explicitly before but is essentially due to Frolenkov–Soundararajan.
|Number of pages||4|
|Journal||Monatshefte fur Mathematik|
|Publication status||Published - 24 Mar 2018|
- Character sums
- Number of divisors
- Quadratic polynomial
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