LOWER ESTIMATES FOR THE GROWTH OF THE FOURTH AND THE SECOND PAINLEVÉ TRANSCENDENTS

Let $w(z)$ be an arbitrary transcendental solution of the fourth (respectively, second) Painlevé equation. Concerning the frequency of poles in $|z|\le r$, it is shown that $n(r,w)\gg r^2$ (respectively, $n(r,w)\gg r^{3/2}$), from which the growth estimate $T(r,w)\gg r^2$ (respectively, $T(r,w)\gg r...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 47; no. 1; pp. 231 - 249
Main Author Shimomura, Shun
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2004
Subjects
characteristic function
elliptic functions
growth order
Painlevé transcendents
growth order
characteristic function
Painlevé transcendents
elliptic functions
Online AccessGet full text
ISSN0013-0915
1464-3839
DOI10.1017/S0013091503000440

Cover

More Information
Summary:Let $w(z)$ be an arbitrary transcendental solution of the fourth (respectively, second) Painlevé equation. Concerning the frequency of poles in $|z|\le r$, it is shown that $n(r,w)\gg r^2$ (respectively, $n(r,w)\gg r^{3/2}$), from which the growth estimate $T(r,w)\gg r^2$ (respectively, $T(r,w)\gg r^{3/2}$) immediately follows. AMS 2000 Mathematics subject classification: Primary 34M55; 34M10
Bibliography:PII:S0013091503000440
ark:/67375/6GQ-1G53HL8P-5
ArticleID:00044
istex:F85112866EF17ED656148EB4376CA579C122D5E3
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091503000440