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

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 .

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.

@article{AIF_1980__30_2_79_0,
     author = {Pichorides, S. K.},
     title = {On the $L^1$ norm of exponential sums},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {30},
     number = {2},
     year = {1980},
     pages = {79-89},
     doi = {10.5802/aif.785},
     zbl = {0432.42001},
     mrnumber = {81j:10058},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1980__30_2_79_0}
}
Pichorides, S. K. On the $L^1$ norm of exponential sums. Annales de l'Institut Fourier, Volume 30 (1980) no. 2, pp. 79-89. doi : 10.5802/aif.785. http://www.numdam.org/item/AIF_1980__30_2_79_0/

[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 80d:10057a | Zbl 0408.10025

[3] S. K. Pichorides, On a conjecture of Littlewood concerning exponential suns (II), Bull. Greek Math. Soc., Vol. 19 (1978), 274-277. | MR 80d:10057b | Zbl 0421.10025

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