Analytic and Probabilistic Methods in Number Theory (eBook)

i-iv -- CONTENTS -- PREFACE -- Part One. ALGEBRAIC NUMBER THEORY -- GEL’FOND’S TRANSCENDENCE METHOD BY ELEMENTARY MEANS -- ALGEBRAIC CONJUGATES OUTSIDE THE UNIT CIRCLE -- APPLICATIONS OF ALGEBRAIC UNITS -- ON SOME DIOPHANTINE EQUATIONS CONNECTED WITH PELLIAN EQUATION -- Part Two. QUADRATIC FORMS -- ON THE GENERAL UNIMPROVABLE ESTIMATES OF THE SINGULAR SERIES OF POSITIVE QUADRATIC FORMS -- ON THE REPRESENTATION OF NUMBERS BY CERTAIN QUADRATIC FORMS IN TEN VARIABLES -- Part Three. ZETA AND L-FUNCTIONS -- THE UNIVERSALITY THEOREM WITH WEIGHT FOR THE LERCH ZETA-FUNCTION -- THE GENERAL ADDITIVE DIVISOR PROBLEM AND MOMENTS OF THE ZETA-FUNCTION -- THE CORRESPONDENCE BETWEEN A DIRICHLET SERIES AND ITS COEFFICIENTS -- A NOTE ON THE MEAN SQUARE OF ?(s) IN THE CRITICAL STRIP -- EXPLICIT FORMULAS AND ASYMPTOTIC EXPANSIONS FOR CERTAIN MEAN SQUARE OF HURWITZ ZETA-FUNCTIONS. II -- ON LIMIT DISTRIBUTION OF THE LERCH ZETA-FUNCTION -- THE FOURTH MOMENTS OF DIRICHLET SERIES -- Part Four. MULTIPLICATIVE NUMBER THEORY -- ESTIMATION OF A CERTAIN FUNCTION RELATED TO THE DIRICHLET DIVISOR PROBLEM -- ON SOME PAIRS OF MULTIPLICATIVE FUNCTIONS CORRELATED BY AN EQUATION -- A CHARACTERIZATION OF SOME ADDITIVE ARITHMETICAL FUNCTIONS -- ON PSEUDOSQUARES -- A REMARK ON SOME SPECIAL ARITHMETICAL FUNCTIONS -- MODIFIED ZETA FUNCTIONS AND THE NUMBER OF g-INTEGERS -- Part Five. VALUE DISTRIBUTION OF ARITHMETIC FUNCTIONS -- ON A CONJECTURE BY ERDÖS AND ITS EXTENSION TO ADDITIVE FUNCTIONS ON THE SET OF PAIRS OF INTEGERS -- MULTIPLICATIVE FUNCTIONS AND STOCHASTIC PROCESSES -- CONVOLUTIONS OF THE POISSON LAWS IN NUMBER THEORY -- SHIFTED PRIMES AND KUBILIUS MODELS -- THE DISTRIBUTION OF THE NUMBER OF PRIME DIVISORS OF NUMBERS OF FORM ab + 1 -- MULTIPLICATIVE FUNCTIONS OF FAREY FRACTIONS -- ON SOME INEQUALITIES IN THE PROBABILISTIC NUMBER THEORY -- THE ASYMPTOTICAL EXPANSION IN THE MEAN VALUE THEOREM FOR MULTIPLICATIVE FUNCTIONS -- LOCAL DISTRIBUTIONS OF ARITHMETIC FUNCTIONS ON SEMIGROUPS -- THE MEAN VALUES OF MULTIPLICATIVE FUNCTIONS. III -- ON THE CONVERGENCE TO THE POISSON LAW -- Part Six. PROBABILISTIC THEORY OF NUMBER SYSTEMS AND SERIES -- RENORMALIZATION OF ALGORITHMS IN THE PROBABILISTIC SENSE -- PROBABILISTIC THEORY OF ADDITIVE FUNCTIONS RELATED TO SYSTEMS OF NUMERATION -- ON LIMIT THEOREMS FOR ENDOMORPHISMS OF A. RÉNYI TYPE -- DENSITIES FOR SUMS OF INDEPENDENT RANDOM VARIABLES AND THEIR APPLICATIONS TO THE VALUE DISTRIBUTIONS OF ?(x), P(x) AND ?(s) -- Part Seven. MISCELLANEOUS -- NOTE ON THE TRANSCENDENCE OF A GENERATING FUNCTION -- SOLUTION OF THE EQUATIONS OF DYNAMICAL CHAOS -- LOGISTIC DIFFERENTIAL EQUATION OF NEUTRAL TYPE -- A THEOREM OF MÜNTZ TYPE FOR CHEBYSHEV POLYNOMIALS -- COMPLETE SYSTEMS OF HOLOMORPHIC FUNCTIONS -- Programme of the Conference