Geodesic
On~a~problem of Littlewood
Izvestiya. Mathematics , Tome 18 (1982) no. 2, pp. 205-225

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The Littlewood conjecture is proved: for any integers $m_1,\dots,m_M$ $$ \int_{-\pi}^{\pi}\biggl|\sum_{j=1}^M\exp(im_jx)\biggr|\,dx\geqslant C\ln M, $$ where $C>0$ is an absolute constant. Bibliography: 19 titles. 
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     author = {S. V. Konyagin},
     title = {On~a~problem of {Littlewood}},
     journal = {Izvestiya. Mathematics },
     pages = {205--225},
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     number = {2},
     year = {1982},
     language = {en},
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S. V. Konyagin. On~a~problem of Littlewood. Izvestiya. Mathematics , Tome 18 (1982) no. 2, pp. 205-225. http://geodesic.mathdoc.fr/item/IM2_1982_18_2_a0/