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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.

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Computing an arithmetic constant related to the ring of Gaussian integers
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by F. Gramain and M. Weber PDF
Math. Comp. 44 (1985), 241-250 Request permission

Corrigendum: Math. Comp. 48 (1987), 854.


We compute the analogue for ${\mathbf {Z}}[i]$ of Euler’s constant, that is $\delta = {\lim _{n \to + \infty }}{\delta _n}$, where ${\delta _n} = ({\Sigma _{2 \leqslant k \leqslant n}}1/\pi r_k^2) - \log n$. For this purpose we give an estimate for \[ {r_k} = \min \left \{ {r \geqslant 0;{\text {there exists}}\;z \in {\mathbf {C}}\;{\text {such that card}}({\mathbf {Z}}[i] \cap \bar D(z,r)) \geqslant k} \right \},\] and we compute a great number of values of ${r_k}$.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Math. Comp. 44 (1985), 241-250
  • MSC: Primary 11D99; Secondary 11J99, 11Y60, 30D15
  • DOI:
  • MathSciNet review: 771043