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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


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 ${r_k}$.
    M. Berger, Géométrie, CEDIC, Paris; Nathan Information, Paris, 1978. H. Chaix, "Sur les points entiers voisins d’une courbe plane convexe-application," Journées de Théorie Analytique et Elémentaire des Nombres, Reims, 1981 and private communication.
  • Jean Dieudonné, Calcul infinitésimal, Hermann, Paris, 1968 (French). MR 0226971
  • A. O. Gel’fond, "Sur les propriétés arithmétiques des fonctions entières," Tôhoku Math. J., v. 30, 1929, pp. 280-285.
  • François Gramain, Sur le théorème de Fukasawa-Gel′fond-Gruman-Masser, Seminar on Number Theory, Paris 1980-81 (Paris, 1980/1981) Progr. Math., vol. 22, Birkhäuser Boston, Boston, MA, 1982, pp. 67–86 (French). MR 693311
  • G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, Clarendon Press, Oxford, 1971.
  • David Masser, Sur les fonctions entières à valeurs entières, C. R. Acad. Sci. Paris Sér. A-B 291 (1980), no. 1, A1–A4 (French, with English summary). MR 590974
  • G. Pólya and G. Szegő, Problems and theorems in analysis. Vol. II, Revised and enlarged translation by C. E. Billigheimer of the fourth German edition, Die Grundlehren der mathematischen Wissenschaften, Band 216, Springer-Verlag, New York-Heidelberg, 1976. Theory of functions, zeros, polynomials, determinants, number theory, geometry. MR 0396134
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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