Vol. 4 Analytic and Probabilistic Methods in Number Theory: Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23–27 September 1996

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Vol. 4 Analytic and Probabilistic Methods in Number Theory

Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23–27 September 1996

Edited by: , and

Part of the multi-volume work

New Trends in Probability and Statistics

Language: English

Published/Copyright: 1997

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Topics

Mathematics Algebra and Number Theory

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i-iv
i

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CONTENTS
v

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PREFACE
viii

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Part One. ALGEBRAIC NUMBER THEORY
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GEL’FOND’S TRANSCENDENCE METHOD BY ELEMENTARY MEANS
3
PETER BUNDSCHUH

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ALGEBRAIC CONJUGATES OUTSIDE THE UNIT CIRCLE
11
ARTŪRAS DUBICKAS

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APPLICATIONS OF ALGEBRAIC UNITS
23
CONSTANTINE KLIORYS

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ON SOME DIOPHANTINE EQUATIONS CONNECTED WITH PELLIAN EQUATION
27
D. A. MITKIN

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Part Two. QUADRATIC FORMS
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ON THE GENERAL UNIMPROVABLE ESTIMATES OF THE SINGULAR SERIES OF POSITIVE QUADRATIC FORMS
35
G. GOGISHVILI

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ON THE REPRESENTATION OF NUMBERS BY CERTAIN QUADRATIC FORMS IN TEN VARIABLES
45
T. VEPKHVADZE and N. TSALUGELASHVILI

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Part Three. ZETA AND L-FUNCTIONS
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THE UNIVERSALITY THEOREM WITH WEIGHT FOR THE LERCH ZETA-FUNCTION
59
R. GARUNKŠTIS

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THE GENERAL ADDITIVE DIVISOR PROBLEM AND MOMENTS OF THE ZETA-FUNCTION
69
ALEKSANDAR IVIĆ

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THE CORRESPONDENCE BETWEEN A DIRICHLET SERIES AND ITS COEFFICIENTS
91
MATTI JUTILA

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A NOTE ON THE MEAN SQUARE OF Ϛ(s) IN THE CRITICAL STRIP
107
A. KAČĖNAS

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EXPLICIT FORMULAS AND ASYMPTOTIC EXPANSIONS FOR CERTAIN MEAN SQUARE OF HURWITZ ZETA-FUNCTIONS. II
119
MASANORI KATSURADA and KOHJI MATSUMOTO

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ON LIMIT DISTRIBUTION OF THE LERCH ZETA-FUNCTION
135
A. LAURINČIKAS

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THE FOURTH MOMENTS OF DIRICHLET SERIES
149
A. I. VINOGRADOV

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Part Four. MULTIPLICATIVE NUMBER THEORY
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ESTIMATION OF A CERTAIN FUNCTION RELATED TO THE DIRICHLET DIVISOR PROBLEM
171
JUN FURUYA and YOSHIO TANIGAWA

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ON SOME PAIRS OF MULTIPLICATIVE FUNCTIONS CORRELATED BY AN EQUATION
191
I. KÁTAI and Β. M. PHONG

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A CHARACTERIZATION OF SOME ADDITIVE ARITHMETICAL FUNCTIONS
205
JEAN-LOUP MAUCLAIRE

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ON PSEUDOSQUARES
213
A. SCHINZEL

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A REMARK ON SOME SPECIAL ARITHMETICAL FUNCTIONS
221
WOLFGANG SCHWARZ and JÜRGEN SPILKER

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MODIFIED ZETA FUNCTIONS AND THE NUMBER OF g-INTEGERS
247
E. STANKUS

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Part Five. VALUE DISTRIBUTION OF ARITHMETIC FUNCTIONS
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ON A CONJECTURE BY ERDÖS AND ITS EXTENSION TO ADDITIVE FUNCTIONS ON THE SET OF PAIRS OF INTEGERS
261
GUTTI JOGESH BABU

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MULTIPLICATIVE FUNCTIONS AND STOCHASTIC PROCESSES
271
G. BAREIKIS

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CONVOLUTIONS OF THE POISSON LAWS IN NUMBER THEORY
283
D. BEKELIS

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SHIFTED PRIMES AND KUBILIUS MODELS
297
P. D. T. A. ELLIOTT

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THE DISTRIBUTION OF THE NUMBER OF PRIME DIVISORS OF NUMBERS OF FORM ab + 1
313
P. D. T. A. ELLIOTT and A. SÁRKÖZY

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MULTIPLICATIVE FUNCTIONS OF FAREY FRACTIONS
323
K.-H. INDLEKOFER and V. STAKĖNAS

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ON SOME INEQUALITIES IN THE PROBABILISTIC NUMBER THEORY
345
JONAS KUBILIUS

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THE ASYMPTOTICAL EXPANSION IN THE MEAN VALUE THEOREM FOR MULTIPLICATIVE FUNCTIONS
357
A. MAČIULIS

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LOCAL DISTRIBUTIONS OF ARITHMETIC FUNCTIONS ON SEMIGROUPS
363
RIMANTAS SKRABUTĖNAS

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THE MEAN VALUES OF MULTIPLICATIVE FUNCTIONS. III
371
GEDIMINAS STEPANAUSKAS

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ON THE CONVERGENCE TO THE POISSON LAW
389
J. ŠIAULYS

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Part Six. PROBABILISTIC THEORY OF NUMBER SYSTEMS AND SERIES
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RENORMALIZATION OF ALGORITHMS IN THE PROBABILISTIC SENSE
401
P. HUBERT and Y. LACROIX

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PROBABILISTIC THEORY OF ADDITIVE FUNCTIONS RELATED TO SYSTEMS OF NUMERATION
413
E. MANSTAVIČIUS

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ON LIMIT THEOREMS FOR ENDOMORPHISMS OF A. RÉNYI TYPE
431
G. MISEVIČIUS

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DENSITIES FOR SUMS OF INDEPENDENT RANDOM VARIABLES AND THEIR APPLICATIONS TO THE VALUE DISTRIBUTIONS OF Δ(x), P(x) AND ς(s)
441
MASUMI NAKAJIMA

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Part Seven. MISCELLANEOUS
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NOTE ON THE TRANSCENDENCE OF A GENERATING FUNCTION
461
JEAN-PAUL ALLOUCHE

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SOLUTION OF THE EQUATIONS OF DYNAMICAL CHAOS
467
F. IVANAUSKAS, T. MEŠKAUSKAS1 and B. KAULAKYS

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LOGISTIC DIFFERENTIAL EQUATION OF NEUTRAL TYPE
475
D. ŠVITRA

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A THEOREM OF MÜNTZ TYPE FOR CHEBYSHEV POLYNOMIALS
485
ROLF WALLISSER

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COMPLETE SYSTEMS OF HOLOMORPHIC FUNCTIONS
489
ROLF WALLISSER

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Programme of the Conference
500

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

February 14, 2012

eBook ISBN:

9783110944648

Edition:

Reprint 2012

Pages and Images/Illustrations in book

Front matter:

7

Main content:

501

Other:

1 Frontispice and num. ill.

https://doi.org/10.1515/9783110944648

eBook ISBN: 9783110944648

Keywords for this book

Stochastik; Zahlentheorie

Vol. 4 Analytic and Probabilistic Methods in Number Theory

Overview

Topics

Table of contents

i-iv

CONTENTS

PREFACE

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

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

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 Ϛ(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

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

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

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 Δ(x), P(x) AND ς(s)

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

Bibliographic data