Absolute convergence exponent of singular integral114 Absolute convergence exponent of singular series114 Accuracy of estimate for multiple trigonometric integral34 Accuracy of estimate in the mean value theorem178 Analog of Bertrand postulate (Chebyshev theorem)104 Analog of Waring's problem for congruences97 Artin problem of representing zero by a form361 Asymptotic formula for the mean value of multiple integral312 Asymptotic formula for the mean value of multiple trigonometric sum210 Cauchy's inequality537 Complete rational multiple trigonometric sum73 Complete rational trigonometric sum modulo q48 Complete system of equations20146 Convergence exponent for singular integrals in multidimensional problems47 Convergence exponent of improper integral20 Dirichlet theorem236 Essentially singular point133 Estimate for double trigonometric sums271 Estimate for the Hardy — Littlewood function G(n)94 Estimates for multiple trigonometric sums181200311 Estimates of special trigonometric sums on small arcs385 First main lemma240 Fundamental lemma155 Fundamental recursive inequality in p-adic method104 Hilbert — Kamke problem316 Incomplete system of equations20146 Jagged polynomial66 Joint distributions of fractional parts of several polynomials228233 Lemma on the number of solutions of a complete system of congruences148150 Lemma on the recurrence inequality172 Linnik's lemma104 Mean value of complete rational trigonometric sum5977 Mean value theorem for multiple trigonometric sums of general form167174 Mean value theorem for r-fold trigonometric sum144163 Modulus belonging to a point133 Multidimensional additive problem353 Multiple trigonometric integrals30