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The “pits effect” for functions in the unit circle

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References

  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.

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  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.

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  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.

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Dedicated to Professor L. J. Mordell on his 80th birthday.

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Littlewood, J.E. The “pits effect” for functions in the unit circle. J. Anal. Math. 23, 237–268 (1970). https://doi.org/10.1007/BF02795503

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