Geodesic
Multiplicative Bounds for $L_1$-Norms of Exponential Sums
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 49-57

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This paper is a sequel of the author's papers [1]–[8] devoted to lower multiplicative bounds on $L_1$ norms and their applications. Now we give estimates for $L_1$ norms of exponential sums and prove the result announced in the paper [8]. 
@article{CMFD_2007_25_a4,
     author = {S. V. Bochkarev},
     title = {Multiplicative {Bounds} for $L_1${-Norms} of {Exponential} {Sums}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {49--57},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_25_a4/}
}
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S. V. Bochkarev. Multiplicative Bounds for $L_1$-Norms of Exponential Sums. Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 49-57. http://geodesic.mathdoc.fr/item/CMFD_2007_25_a4/