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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

Abstract:

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: https://doi.org/10.1090/S0025-5718-1985-0771043-3
  • MathSciNet review: 771043