Abstract:
Estimates of multiple trigonometric sums similar to the modern estimate of the zeta-sum are obtained. This allows us to estimate trigonometric sums twisted with the multivariate divisor function and corresponding sums with primes.
Key words:multiple trigonometric sums, Dirichlet's characters, trigonometric sums twisted with the multivariate divisor function, analogue of the zeta-sum with primes, mean-value theorem for multiple trigonometric sums.
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