On~a~problem of Littlewood

S. V. Konyagin

Izvestiya. Mathematics , Tome 18 (1982) no. 2, pp. 205-225.

Résumé

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.

Bibliographie

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