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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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.


Poisson approximation and Weibull asymptotics in the geometry of numbers
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by Michael Björklund and Alexander Gorodnik PDF
Trans. Amer. Math. Soc. 376 (2023), 2155-2180 Request permission


Minkowski’s First Theorem and Dirichlet’s Approximation Theorem provide upper bounds on certain minima taken over lattice points contained in domains of Euclidean spaces. We study the distribution of such minima and show, under some technical conditions, that they exhibit Weibull asymptotics with respect to different natural measures on the space of unimodular lattices in $\mathbb {R}^d$. This follows from very general Poisson approximation results for shrinking targets which should be of independent interest. Furthermore, we show in the appendix that the logarithm laws of Kleinbock-Margulis [Invent. Math. 138 (1999), pp. 451–494], Khinchin and Gallagher [J. London Math. Soc. 37 (1962), pp. 387–390] can be deduced from our distributional results.
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Additional Information
  • Michael Björklund
  • Affiliation: Mathematical Sciences, Chalmers, Chalmers Tvärgata 3, 412 58 Gothenburg, Sweden
  • Email:
  • Alexander Gorodnik
  • Affiliation: Department of Mathematics, University of Zürich, Winterthurerstrasse 190, CH-8057, Switzerland
  • MR Author ID: 649826
  • Email:
  • Received by editor(s): January 14, 2022
  • Received by editor(s) in revised form: September 15, 2022, and September 15, 2022
  • Published electronically: December 8, 2022
  • Additional Notes: The first author was supported by GoCas Young Excellence grant 11423310 and Swedish VR-grant 11253320, the second author was supported by the SNF grant 200021–182089.
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 376 (2023), 2155-2180
  • MSC (2020): Primary 37A50; Secondary 37A25, 60G70
  • DOI:
  • MathSciNet review: 4549702