Final announcement

The 15th Czech and Slovak International Conference on Number Theory

Ostravice (Czech Republic), Hotel Montér
September 3. - 8., 2001

Organized by the

Department of Mathematics of the Faculty of Sciences of the University of Ostrava

Department of Mathematics, Institute of Chemical Technology, Prague

Department of Mathematics, Masaryk’s University of Brno

Department of Mathematical Analysis, Charles University, Prague

Mathematical institute of Slovak Academy of Scientes, Bratislava



The following mathematicians confirmed the participation

Takashi Agoh, Japan
Jannis A. Antoniadis, Greece
Antal Bege, Romania
Kurt Girstmair, Austria
Alain Escassut, France
Peter Grabner, Austria
Cornelius Greither, Germany
Georges Grekos, France
Kálman Gyory, Hungary
Franz Halter - Koch, Austria
Terence Jackson, United Kingdom
Anatoly Karatsuba, Russia
Günter Lettl, Austria
Claude Levesque, Canada
Jan Mináč, Canada
Wladyslaw Narkiewicz, Poland
Jan Nekovář, United Kingdom
Attila Petho, Hungary
Andrzej Schinzel, Poland
Iliya Slavutskii, Israel
Kazimierz Szymiczek, Poland


Lubomir Alexandrov, Russia
Attila Berczes, Hungary
Daniel Berend, Israel
Victor Beresnevich, Belarus
Vasily Bernik, Belarus
Michal Bulant, Czech Republic
James Carter, Charleston
Marzena Ciemala, Poland
ALfred Czogala, Poland
Jiří Čížek, Czech Republic
Cristian D. Popescu, USA
Anton Deitmar, United Kingdom
Ilaria Del Corso, Italy
Karl Dilcher, Canada
Zuzana Divisova, Czech Republic
Pavla Drábková, Czech Republic
Roberto Dvornicich, Italy
Věra Dvořáková, Czech Republic
Joseph K. Essilfie, Ghana
Sophie Frisch, Austria
Petr Fuchs, Czech Republic
István Gaál, Hungary
Lajos Hajdu, Hungary
Jaroslav Hančl, Czech Republic
Richard Hill, England
Mikihito Hirabayashi, Japan
Syed Furgan Ullah Hussaini, UAE
Mostafa Ibrahim, Egypt
Stanislav Jakubec, Slovakia
Istvan Jarasi, Hungary
Aleka Kalapodi, Greece
Yaroslav Kholjavka, Ukraine
Helmut Koch, Germany
Attila Komzsik, Slovakia
Petra Konečná, Czech Republic
Angeliki Kontolatou, Greece
Juraj Kostra, Czech Republic
Ella Kovalevskaya, Belarus
Jan Krempa, Poland
Michal Křížek, Czech Republic
Radan Kučera, Czech Republic
Jitka Kuhnová, Czech Republic
Mieczyslaw Kula, Poland
Mario Lamberger, Austria
Erich Lamprecht, Germany
Aini Laoudi, Algerie
Claude Levesque, Canada
Stephane Louboutin, France
Ladislav Mišík, Czech Republic
Jiří Močkoř, Czech Republic
Karol Nemoga, Slovakia
Břetislav Novák, Czech Republic
Mikhail Novikov, Russia
Gábor Nyul, Hungary
Peter Olajos, Hungary
Petr Otipka, Czech Republic
Milan Paštéka, Slovakia
Istvan Pink, Hungary
Akos Pinter, Hungary
Marek Pomp, Czech Republic
Štefan Porubský, Czech Republic
Csaba Rakaczki, Hungary
Agbeko Tsikata Ransford, Ghana
Thangadurai Ravindranathan, India
Andrzej Rotkiewicz, Poland
Selmane Schehrazad, Algeria
Ladislav Skula, Czech Republic
Andrzej Sladek, Poland
Lawrence Sommer, USA
Laszlo Szalay, Hungary
Jaroslav Šeibert, Czech Republic
John Stabakis, Greece
Oto Strauch, Bratislava
Herendi Tamas, Hungary
Szabolcs Tengely, The Netherland
Nobuhiro Terai, Japan
Jörg Thuswaldner, Austria
Witold Tomaszewski, Poland
János Tóth, Slovakia
Larisa Trelina, Belarus
Pavel Trojovský, Czech Republic
Michal Vavros, Czech Republic
Denis Vasilyev, Belarus
Lev Vsevold, Israel
Reinhard Winkler, Austria
Takao Yamazaki, Japan





The conference will be opened on Monday morning, September 3rd, and finished on Saturday at noon, September 8th. Sunday, September 2nd , is the arrival day.

There will be some invited plenary lectures (45 minutes) as well as contributed talks (20 minutes). Problem Section will be organized. Program in sections is only tentative. The third section might be opened.


The following plenary lectures are assumed to be presented:

Carter James


Hilbert-Speiser number fields of given type

Escassut Alain


p-adic Nevanlinna Theory and applications

Grabner Peter


Digital function and its applications

Greither Cornelius


Recent work on the Brumer-Stark conjecture concerning annihilation of class groups

Halter- Koch Franz


Representation of prime powers by binary quadratic forms

Jannis A. Antoniadis


Prime powers represented by quadratic forms

Kálman Gyory


Bounds for the numbers of solutions of decomposable polynomial equations

Karatsuba Anatoly


On the fractional parts of the fast increasing functions

Mináč Jan


Galois, Witt and Voevodsky

Narkiewicz Wladyslaw


Primes represented by reducible quadratic polynomials

Nekovář Jan

United Kingdom

On the parity of ranks of Selmer groups

Schinzel Andrzej


Evaluation of a certain arithmetic sum


The following titles of contributed talks have been announced till the end of June, 2001.

Agoh Takashi


Some topics on the relative class number of cyclotomic fields

Alexandrov Lubomir


Recurring Eratosthenes sieve and plane prime number geometry

Bege Antal


Some inequalities concerning arithmetical functions

Beresnevich Victor


Diophantine approximation on curves over the field of complex numbers

Bulant Michal

Czech Republic

On the parity o the class number of the field Q(,,,)

Corso Ilaria


On the index of a number field

Czogala Alfred


Witt ring of a global field

Dilcher Karl


Bernoulli numbers and confluent hypergeometric functions

Divisova Zuzana

Czech Republic

On polynomial cycles in cubic fields

Dvornicich Roberto


Bounds for the height and size of the ideal class group in CM-fields

Frisch Sophie


On integer-valued polynomials

Fuchs Petr

Czech Republic

Bernoulli numbers and binary trees

Gaal Istvan


Power integral bases in algebraic number fields

Grekos Georges


Removing elements from additive bases

Hill Richard


Metaplectic covers of GLn and the Gauss-Schering Lemma

Hirabayashi Mikihito


Inkeri`s determinant for an imaginary abelian number field

Jackson Terence

United Kingdom

An Improved bound in a problem about quaternary forms

Kovalevskaya Ella


p-adic variant of Khintchine’s theorem for the curves in


Koch Helmut


Maximal 2-extensions with given ramification points

Krempa Jan


On completely unisotropic modules

Komzsik Attila


Křížek Michal

Czech Republic

Necessary and sufficient conditions for the primality of Fermat numbers

Konečná Petra

Czech Republic

On polynomial cycles in finite fields

Levesque Claude


A fundamental system of units of certain fields of degree 4 over Q

Louboutin Stephane


Exponents of the ideal class groups of CM number fields

Lettl Günter


On families of Thue equations

Laoudi Aini


Power integral bases in cubic cyclic number field

Mostafa Ibrahim


New recurrence relations to well-known sequences

Nobuhiro Terai


On diophantine equation related to Eisenstein numbers

Novikov Mikhail


Generalization of Bunyakovsky theorem in cases of simple and composite radicals and the applications to diophantine equations

Nyul Gábor


Power integral bases in biquadratic number fields

Pezda Tadeus


On cycles and precycles of polynomial mapping Z2® Z2

Porubský Štefan

Czech Republic

will be specified later

Schehrazad Selmane


Quadratic Extensions of Quintic Fields of Signature (3,1)

Sladek Andrzej


Witt ring of a global field

Slavutskii Iliya


Ankeny-Artin - Chowla conjecture: history, computation and its equivalents

Somer Lawrence


On Special Multipliers of k-th-Order Linear Recurrences Modulo pr

Szalay Laszlo


The diophantine equation 2n+2m+1=x2

Šeibert Jaroslav

Czech Republic

On properties and relations of some types of the numbers derived from Bernoull´s inequality

Trelina Larisa


On the k-free factors of values of polynomials

Takao Yamazaki


Tate duality and ramification of division algebra

Trojovský Pavel

Czech Republic

On properties and relations of some types of the numbers derived from Bernoull´s inequality

Vasilyev Denis


Diophantine approximation on curves over the field of complex numbers

Vavros Michal

Czech Republic

On polynomial cycles in the ring of circulant matrices



The Proceedings of the conference will be published as a special issue of the journal Acta Mathematica et Informatica Universitatis Ostraviensis in 2002. The papers should be submitted in AMSTeX or another TEX format (as a file surname.TEX). The deadline for sending the paper will be on January 30, 2002. The author of a paper accepted for publication will receive a free copy of the journal and 25 free reprints. All papers submitted for publication will be reviewed. The participants will receive the detail information about this publication during the conference.



As it was mentioned in the first announcement, the conference will take place in a mountain centre “Ostravice” in a Hotel Montér. The registration office will be at the hotel “Montér”.



By plane:

Participants can use domestic flights from Praque to Ostrava airport. Departures from Prague are September 2nd : 12.40, 21.40, September 3rd : 12.40, 21.40 and time of arrivals of these flights is :

September 2nd : 13.40, 22.40

September 3rd : 13.40, 22.40

A transport will be organized from the Ostrava airport to the hotel “Montér” starting from September 2nd.


By train:

Participants can use any domestic or international train connection to Ostrava - Main Station. A transport from the Main Station will be organized on Sunday 2nd from 12.00 a.m. to 10.00 p.m., and on September 3rd , from. 8.00 a.m. to 2.00 p.m..


For the better organisation please let us know the time of your arrival to Ostrava-Main Station and Ostrava airport if you would like to use our transport to Ostravice.


If you want vegetarian meals, please let us know your specific requirements to address


By car:

From Ostrava take direction of Frýdek-Místek, Frýdlant nad Ostravicí and Ostravice. In Ostravice, at the hotel FREUD you take direction across the railway to the mountains. Hotel MONTER is about 5 minutes by car.


Hotel Monter
Telephone: 00420-658-682108
Fax: 00420-658-682161

In the hotel Monter, there are swimming pool, sauna and also masseur. There will be organized a trip (specified at the beginning of the conference, a tourist trip or visiting different places in North Moravia region). For accompanying persons a programme will be organized during the whole week.


Department of Mathematics
University of Ostrava
30. dubna 22
CZ-701 03 Ostrava 1
Czech Republic