## New Trends in Probability and Statistics: Analytic and probabilistic methods in number theory, proceedings of the International Conference in honour of J. Kubilius, Palanga, Lithuania, 24 - 28 September 1991 |

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### Contents

A Theorem of Gelfond via Schneiders Method | 9 |

An Estimation of the Difference Between Two Zeros of a Polynomial | 17 |

On the Arithmetic Properties of the Values of Functions | 23 |

Approximation of Irrationals by rnn Satisfying f mna | 31 |

Discriminants of Decomposable Forms | 39 |

On Some Entire Modular Forms of Half Integral | 57 |

On Solutions of Linear Congruences | 69 |

The Method of Trigonometric Sums and Lower Estimates | 75 |

Smoothness of the Distributions of Arithmetic Functions | 191 |

Additive Arithmetic Functions and Processes | 211 |

Topics on Arithmetic Functions with Rational Arguments | 235 |

Measure Theory and Arithmetical Functions | 251 |

Generalizations of Kubilius Class of Additive Functions I | 269 |

The MultiDimensional Local Theorem for Additive Arithmetic Functions | 285 |

The von Mises Theorem in Number Theory | 293 |

The Law of Large Numbers in the Case of Shifted Primes | 311 |

The Optimal Zone for Large Deviations of the Denominators | 83 |

Ergodic Properties of MultiDimensional Subtractive Algorithms | 91 |

Selbergs Inequality in Arithmetic Progressions | 103 |

The Mean Values of Multiplicative Functions Defined | 121 |

Semigroup Elements Free of Large Prime Factors | 135 |

On Multiplicative Functions with Regularity Properties | 155 |

Distribution of Prime Vectors in Integral Lattices | 173 |

On Some Formulae in Analytic Number Theory II | 319 |

The Atkinson Formula Near the Critical Line | 335 |

Large Value Estimates for Hecke Polynomials | 355 |

On Normal Bases of Algebraic Number Fields | 369 |

Number Theory and Number Crunching | 379 |

List of Contributors | 387 |

### Common terms and phrases

ABSTRACT Acta Arithm additive arithmetic functions additive functions algebraic number field algebraically homogeneously algebraically algebraically independent algorithm analytic Aparicio Bernardo arbitrary Arithm assertion Assume Babu Banach space binary forms bound coefficients consider continued fractions Corollary decomposable forms Dedekind domain definition denote deviation from zero Diophantine approximation discriminant distribution function equal equation estimate Evertse and Gyory exists Fainleib finite form F functions defined Gelfond Gyory Hence implies inequality interval Kubilius lattice limit distribution limit theorem linear forms linearly independent Lithuania Lomadze Manstavicius Eds matrix Mauclaire measure method Mobius function multiplicative function natural numbers Nauk normal basis notations obtain paper polynomial positive integers prime numbers prime vectors Probabilistic Number Theory problem proof of Theorem properties prove random variables real numbers result Russian satisfies the condition Schweiger semigroup sequence Shidlovskii square-free Stakenas Timofeev transcendence degree Tulyaganova values Vilnius University VSP/TEV