Funktsional'nyi Analiz i ego Prilozheniya
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Funktsional. Anal. i Prilozhen.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 1, Pages 30–42
DOI: https://doi.org/10.4213/faa16 (Mi faa16) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the Number of Rational Points on a Strictly Convex Curve

F. V. Petrov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (237 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.4213/faa16
Abstract: Let $\gamma$ be a bounded convex curve on the plane. Then $\#(\gamma\cap(\mathbb{Z}/n)^2)=o(n^{2/3})$. This strengthens the classical result due to Jarník (the upper bound $cn^{2/3}$) and disproves the conjecture on the existence of a so-called universal Jarník curve.
Keywords: convex curve, lattice point, affine length.
Received: 17.01.2005
English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 1, Pages 24–33
DOI: https://doi.org/10.1007/s10688-006-0003-6
Bibliographic databases:
Document Type: Article
UDC: 511.9
Language: Russian
Citation: F. V. Petrov, “On the Number of Rational Points on a Strictly Convex Curve”, Funktsional. Anal. i Prilozhen., 40:1 (2006), 30–42; Funct. Anal. Appl., 40:1 (2006), 24–33
Citation in format AMSBIB
\Bibitem{Pet06}
\by F.~V.~Petrov
\paper On the Number of Rational Points on a Strictly Convex Curve
\jour Funktsional. Anal. i Prilozhen.
\yr 2006
\vol 40
\issue 1
\pages 30--42
\mathnet{http://mi.mathnet.ru/faa16}
\crossref{https://doi.org/10.4213/faa16}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2223247}
\zmath{https://zbmath.org/?q=an:1152.11030}
\elib{https://elibrary.ru/item.asp?id=9200284}
\transl
\jour Funct. Anal. Appl.
\yr 2006
\vol 40
\issue 1
\pages 24--33
\crossref{https://doi.org/10.1007/s10688-006-0003-6}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000236532100003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33644897337}
Linking options:
  • https://www.mathnet.ru/eng/faa16
  • https://doi.org/10.4213/faa16
  • https://www.mathnet.ru/eng/faa/v40/i1/p30
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
    Statistics & downloads:
    Abstract page:779
    Full-text PDF :363
    References:83
    First page:1
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024