论文信息 - Bateman's Constants Reconsidered and the Distribution of Cubic Residues

Bateman's Constants Reconsidered and the Distribution of Cubic Residues

We analyze the computation of certain slowly convergent infinite products in- volving cubic characters. A first-order analysis gives a 2D or 3D answer immediately, but extensive computation of cubic residues only improves this to 5D or 6D. To do better, one must examine the distribution of cubic residues or evaluate certain Dedekind Zeta functions. Both are done. The constants thus obtained are used to examine a variant of the Hardy- Littlewood Conjecture K concerning primes of the form ns + a. Some related mathematics needed and developed includes an answer to this: Which p, satisfying x' - a (mod p), have two solutions x that differ by k (mod p)?

D. Shanks | M. Lal

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