Journal d’Analyse Mathématique

, Volume 23, Issue 1, pp 237–268 | Cite as

The “pits effect” for functions in the unit circle

  • J. E. Littlewood


Unit Circle Integral Function Straightforward Calculation Finite Order Partial Quotient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Nassif, On the behaviour of the function\(f(z) = \sum e^{\surd \bar 2\pi in^2 } \frac{{z^{2_n } }}{{n!}}\) Proc. London Math. Soc.,54 (1954), 201–214.CrossRefMathSciNetGoogle Scholar
  2. 2.
    J. E. Littlewood, The “pits effect” for the integral function\(f(z) = \sum \exp \left\{ { - e^{ - 1} (n \log n - n) + \pi i\alpha n^2 } \right\}z, \alpha = \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} (\sqrt 5 - 1)\) Abhandlungen aus Zahlentheorie und Analysis zur Erinnerung an Edmund Landau (1877–1938), VEB Deutscher Verlag der Wissenschaften, Berlin 1968, 195–215.Google Scholar
  3. 3.
    —, A “pits effect” for all smooth enough integral functions with a coefficient factor\(\exp (n^2 \alpha \pi i) \alpha = \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} (\sqrt 5 - 1)\) J. London Math. Soc.,43 (1968), 79–92.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1970

Authors and Affiliations

  • J. E. Littlewood
    • 1
  1. 1.Department of MathematicsTrinity CollegeCambrigeEngland

Personalised recommendations