## Collection of Articles Dedicated to Academician I. M. Vinogradov on the Eightieth Anniversary of His Birth, Volume 1 |

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### Contents

N N Bogoljubov And V S Vladimirov | 2 |

An application of algebraic number theory to mathematical statistics | 19 |

A linear differential evasion game | 27 |

On subgroups of free periodic groups of odd exponent | 61 |

Dirichlet series with euler product in the theory of siegel modular forms of genus 2 | 70 |

On the theory of quasilinear ordinary differential equations of first order | 94 |

Artin Lseries and the Adele group | 105 |

Artin LSeries and his conjectures | 124 |

Estimates of the difference between distributions in the levy metric | 232 |

On solving operator equations which do not satisfy the conditions of correctness | 241 |

Estimates for trigonometric sums by vinogradovs method and some applications | 251 |

On the traces of functions of several variables and on direction fields regular at infinity for the laplace operator | 266 |

Periodic dirichlet functions with functional equations of riemann type I | 281 |

Monotonic convex matrix loss functions in statistics | 301 |

On the summability of a dirichlet series with complex exponents and its application | 310 |

On class preservation under a differentiable mapping | 339 |

Effective error estimates for difference solutions of boundary value problems in ordinary differential equations | 143 |

Firstorder necessary conditions and axiomatics for extremal problems | 156 |

On stabilization of the solution of the cauchy problem for a parabolic equation with one space variable | 187 |

Extremal problems in the theory of positive quadratic forms | 211 |

Sharpness of the lebesgue estimate for approximation of functions with given modulus of continuity by means of fourier sums | 349 |

On Estimating rational trigonometric sums with prime Denominator | 358 |

Representation of functions of class L By Series | 386 |

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abelian adele group Akad algebraic analytic angle approximate solutions arbitrary Artin L-series assertion assume belongs boundary bounded coefficients compact set cone consider constant continuously differentiable convergence convex convex set corresponding defined definition depend derivatives dimensional Dirichlet functions Dirichlet series Dokl domain elements entire function equal error estimates evasion exists field filter follows formula function F(z functional equation Galois group given halfplane Hecke operators Hence holds holomorphic inequality integral curves intersection interval lattice Lemma linear mapping Math method modular forms modulus modulus of continuity natural number Nauk SSSR non-abelian nonnegative obtain operator parameter plane polyhedron polynomial positive number prime ideals problem proof properties proved quadratic forms rational reciprocity law region G relation representation matrix satisfies the condition sequence space sphere Steklov subgroup subject classifications 1970 subspace sufficient theorem theory topology uniformly with respect variables vector virtue zero