|
VIDEO LIBRARY |
Conference in memory of A. A. Karatsuba on number theory and applications, 2015
|
|||
|
Short exponential sums of Weyl's type Z. Kh. Rakhmonov, F. Z. Rahmonov Institute of Mathematics, Academy of Sciences of Republic of Tajikistan, Dushanbe |
|||
Abstract: The talk is devoted to the investigation of short Weyl's exponential sums of the type $$ T(\alpha;x,y)\,=\,\sum_{x-y<m\leq x}e(\alpha m^n),\quad \alpha\,=\,\frac{a}{q}\,+\,\lambda , \quad (a,q)=1, \quad q\leq \tau ,\quad |\lambda|\,\leq\, \frac{1}{q\tau}, $$ and theirs applications to the problem of distribution of fraction parts of the polinomial with the argument from a short segment, and to some additive problems with almost equal summands. |