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
Multiple trigonometric sums1 Multiple trigonometric sums with summation domains of special form218 Multiplicity of intersection of domains81 p-adic method2 p-adic proof of Vinogradov's theorem on estimating G(n) in the Waring problem378 Recurrence inequality169 Regular point133 Second main lemma289 Set of vectors regular modulo q146147 Set of vectors singular modulo q146147 Simplest properties of Weyl's sum79 Simplified estimate in Vinogradov's mean value theorem132 Singular integral in Tarry's problem20 Singular integral in the Hilbert — Kamke problem114317 Singular integrals in multidimensional problems43 Singular point133 Singular series in multidimensional problems77 Singular series in Tarry's problem2060 Singular series in the Hilbert — Kamke problem114317 Tarry's problem20 Tartakovskii lemma134 Theorems on multiplicity of intersection of multidimensional regions181191 Trigonometric integrals36 U-numbers389 V-numbers379 van der Korput's lemma537 Vectors corresponding to a matrix146 Vinogradov's estimate of Weyl's sum92 Vinogradov's integral80 Vinogradov's lemma on "cups"537 Vinogradov's lemma on the "number of hits"85 Vinogradov's mean value theorem48588 Vinogradov's mean value theorem, Linnik's p-adic proof133 Vinogradov's mean value theorem, p-adic proof104112 Vinogradov's method79 Weil estimate59 Weyl sums179