Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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.

 

Distribution of complex algebraic numbers
HTML articles powered by AMS MathViewer

by Friedrich Götze, Dzianis Kaliada and Dmitry Zaporozhets PDF
Proc. Amer. Math. Soc. 145 (2017), 61-71 Request permission

Abstract:

For a region $\Omega \subset \mathbb {C}$ denote by $\Psi (Q;\Omega )$ the number of complex algebraic numbers in $\Omega$ of degree $\leq n$ and naive height $\leq Q$. We show that \[ \Psi (Q;\Omega )=\frac {Q^{n+1}}{2\zeta (n+1)}\int _\Omega \psi (z) \nu (dz)+O\left (Q^n \right ),\quad Q\to \infty , \] where $\nu$ is the Lebesgue measure on the complex plane and the function $\psi$ will be given explicitly.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11N45, 11C08
  • Retrieve articles in all journals with MSC (2010): 11N45, 11C08
Additional Information
  • Friedrich Götze
  • Affiliation: Department of Mathematics, Bielefeld University, P.O. Box 10 01 31, 33501 Bielefeld, Germany
  • MR Author ID: 194198
  • Email: goetze@math.uni-bielefeld.de
  • Dzianis Kaliada
  • Affiliation: Institute of Mathematics, National Academy of Sciences of Belarus, Surganova Str 11, 220072 Minsk, Belarus
  • MR Author ID: 933471
  • Email: koledad@rambler.ru
  • Dmitry Zaporozhets
  • Affiliation: St. Petersburg Department of Steklov Institute of Mathematics, Fontanka 27, 191011 St. Petersburg, Russia
  • MR Author ID: 744268
  • Email: zap1979@gmail.com
  • Received by editor(s): October 16, 2015
  • Received by editor(s) in revised form: March 17, 2016
  • Published electronically: July 7, 2016
  • Additional Notes: This research was supported by CRC 701, Bielefeld University (Germany).
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 61-71
  • MSC (2010): Primary 11N45; Secondary 11C08
  • DOI: https://doi.org/10.1090/proc/13208
  • MathSciNet review: 3565360