no. 2
On the L 1 norm of exponential sums
Annales de l'Institut Fourier, Tome 30 (1980) no. 2, pp. 79-89.

La norme L 1 d’un polynôme trigonométrique ∑ 1 N a j exp ( in j x), |a j |≥1, dépasse

C ( log N ) / ( log log N ) 2 .

The L 1 norm of a trigonometric polynomial with N non zero coefficients of absolute value not less than 1 exceeds a fixed positive multiple of C( log N)/( log log N) 2 .

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     author = {Pichorides, S. K.},
     title = {On the $L^1$ norm of exponential sums},
     journal = {Annales de l'Institut Fourier},
     pages = {79--89},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {30},
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     year = {1980},
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Pichorides, S. K. On the $L^1$ norm of exponential sums. Annales de l'Institut Fourier, Tome 30 (1980) no. 2, pp. 79-89. doi : 10.5802/aif.785. http://archive.numdam.org/articles/10.5802/aif.785/

[1] J. F. Fourier, On a theorem of Paley and the Littlewood conjecture, To appear in Arkiv för Matematik.

[2] S. K. Pichorides, On a conjecture of Littlewood concerning exponential sums (I), Bull. Greek Math. Soc., Vol. 18 (1977), 8-16. | MR | Zbl

[3] S. K. Pichorides, On a conjecture of Littlewood concerning exponential suns (II), Bull. Greek Math. Soc., Vol. 19 (1978), 274-277. | MR | Zbl

[4] A. Zygmund, Trigonometric Series. Vol. I, II. Cambridge University Press, 1968. October 1979.

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