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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Bateman’s constants reconsidered and the distribution of cubic residues
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by Daniel Shanks and Mohan Lal PDF
Math. Comp. 26 (1972), 265-285 Request permission


We analyze the computation of certain slowly convergent infinite products involving cubic characters. A first-order analysis gives a $2{\text {D}}$ or $3{\text {D}}$ answer immediately, but extensive computation of cubic residues only improves this to ${\text {5D}}$ or ${\text {6D}}$. 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 ${\text {K}}$ concerning primes of the form ${n^3} + a$. Some related mathematics needed and developed includes an answer to this: Which $p$, satisfying ${x^3} \equiv a\pmod p$, have two solutions $x$ that differ by $k\pmod p$?
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 265-285
  • MSC: Primary 10H35
  • DOI:
  • MathSciNet review: 0302590