Department of Mathematics and Statistics
Faculty of Science
Masaryk Univerzity
Kotlářská 2
611 37 Brno
Czech Republic
E-mail: kucera@math.muni.cz
Journals
[1] R. Kučera,
On a certain subideal of
the Stickelberger ideal of a cyclotomic field,
Arch. Math. 22 (1986), 7-20.
[2] R. Kučera, Výpočet diskrétní konvoluce pomocí
číselně teoretických transformací, in Czech,
Elektrotechn. čas. 38 (1987), 50-60.
[3] R. Kučera, Bazis ideala Stickel'bergera
i systema osnovnych krugovych jedinic, in Russian, in Kol'ca i moduli 3,
Zapiski naučnych seminarov LOMI, 175, 69-74,
Nauka, Leningrad 1989.
[4] R. Kučera,
A basis for the Stickelberger ideal and the system of circular units of a
cyclotomic field,
J. Math. Sciences 57 (1991), No.6, 3485-3489. DOI: 10.1007/BF01100117
[5] R. Kučera, On bases of odd and even universal
ordinary distributions, J. Number Theory 40 (1992), 264-283.
[6] R. Kučera, On bases of the Stickelberger ideal
and of the group of circular units of a cyclotomic field,
J. Number Theory 40 (1992), 284-316.
[7] R. Kučera and
K.
Szymiczek, Witt equivalence of
cyclotomic fields,
Math. Slovaca 42 (1992), 663-676.
[8] R. Kučera,
Different groups
of circular units of a compositum of real quadratic fields,
Acta Arithmetica 67 (1994), 123-140.
[9] R. Kučera, On the parity of the class number
of a biquadratic field,
J. Number Theory 52 (1995), 43-52.
[10] R. Kučera and
J. Nekovář,
Cyclotomic units in Zp extensions,
J. Algebra 171 (1995), 457-472.
[11] R. Kučera, On the Stickelberger ideal
and circular units of a compositum of quadratic fields,
J. Number Theory 56 (1996), 139-166.
[12] R. Kučera, A note on Sinnott's definition
of circular units of an abelian field,
J. Number Theory 63 (1997), 403-407.
[13] R. Kučera,
A generalization of a unit index of Greither
, Acta Mathematica et Informatica Universitatis
Ostraviensis 6 (1998), 149-154.
[14] R. Kučera,
On the Stickelberger ideal and circular units of some genus fields,
Tatra Mountains Math. Publ. 20 (2000), 93-104.
[15] R. Kučera,
Formulae for the relative class number of an imaginary
abelian field in the form of a determinant, Nagoya Math. J. 163 (2001),
167-191.
[16]
C. Greither, S. Hachami, and R. Kučera,
Racines d'unites cyclotomiques et divisibilité du nombre de classes d'un
corps abélien réel, Acta Arithmetica 96 (2001), 247-259.
[17]
C. Greither and R. Kučera,
The lifted root number conjecture for fields of prime degree over the
rationals: an approach via trees and Euler systems, Annales de
l'Institut Fourier 52 (2002), 735-777.
[18] R. Kučera,
Formulae for the relative class number of an
imaginary abelian field in the form of a product of determinants,
Acta Mathematica et Informatica Universitatis
Ostraviensis, 10 (2002), 79-83.
[19] R. Kučera,
A Note on Circular Units in Zp-extensions,
Journal de Théorie des Nombres de Bordeaux 15 (2003), 223-229.
[20]
C. Greither, and R. Kučera,
Annihilators for the class group
of a cyclic field of prime power degree, Acta Arithmetica 112 (2004),
177-198.
[21] R. Kučera,
Circular units and class groups of abelian fields,
Ann. Sci. Math. Québec 28 (2004), 121-136.
[22]
C. Greither
and R. Kučera,
Annihilators for the class group
of a cyclic field of prime power degree II,
Canadian Journal of Mathematics 58 (2006), 580-599.
[23]
C. Greither
and R. Kučera,
Annihilators of minus class groups of imaginary abelian fields,
Annales de l'Institut Fourier 57 (2007), 1623-1653.
[24]
C. Greither
and R. Kučera,
On a conjecture concerning minus parts in the style of Gross,
Acta Arithmetica 132 (2008), 1-48.
[25] R. Kučera,
On the Class Number of a Compositum of Real Quadratic Fields: an Approach
via Circular Units, Funct. Approx. Comment. Math. 39 (2008), 179-189.
[26]
C. Greither
and R. Kučera,
The Minus Conjecture revisited, Journal für die Reine und
Angewandte Mathematik 632 (2009), 127-142.
[27] R. Kučera,
On Annihilators of the Class Group of an Imaginary Compositum of Quadratic
Fields, Acta Arithmetica 143 (2010), 257-269.
[28]
M. Bulant and R. Kučera,
On a modification of the group of circular units
of a real abelian field,
J. Number Theory 133 (2013), 3138-3148.
[29]
C. Greither and R. Kučera,
Eigenspaces of the ideal class group, Annales de
l'Institut Fourier 64 (2014), 2165-2203.
[30]
C. Greither and R. Kučera,
Linear forms on Sinnott's module, J. Number Theory 141 (2014), 324-342.
[31]
C. Greither
and R. Kučera,
Annihilators for the class group
of a cyclic field of prime power degree III,
Publicationes Mathematicae
Debrecen 86 (2015), 401-421.
[32] R. Kučera,
The circular units and the Stickelberger ideal of a cyclotomic field revisited,
Acta Arithmetica 174 (2016), 217-238.
[33] R. Kučera and A. Salami,
Circular units of an abelian field ramified at three primes,
J. Number Theory 163 (2016), 296-315, http://dx.doi.org/10.1016/j.jnt.2015.11.023.
[34] R. Kučera,
Revealing two cubic non-residues in a quadratic field locally,
Math. Slovaca 68 (2018), No. 1, 53-56,
https://doi.org/10.1515/ms-2017-0079.
[35] R. Kučera,
On a theorem of Thaine,
J. Number Theory 173 (2017), 416-424,
https://doi.org/10.1016/j.jnt.2016.09.020.
[36]
H. Chapdelaine and R. Kučera,
Annihilators of the ideal class group of a cyclic extension of an imaginary
quadratic field, Canadian Journal of Mathematics 71 (2019), 1395-1419,
http://dx.doi.org/10.4153/CJM-2018-035-9.
[37]
C. Greither
and R. Kučera,
Washington units, semispecial units, and annihilation of class groups,
Manuscripta Mathematica 166 (2021), 277-286.
[38]
C. Greither
and R. Kučera,
On
the compositum of orthogonal cyclic fields of the same odd prime degree,
Canadian Journal of Mathematics 73 (2021), 1506-1530.
[39]
O. Bernard, R. Kučera,
A short basis of the
Stickelberger ideal of a cyclotomic field,
to appear in Mathematics of Computation.
[40]
P. Francírek, R. Kučera,
Annihilators of the ideal class group of an imaginary abelian number field,
to appear in Michigan Mathematical Journal.
Proceedings
[1] R. Kučera, On the bases of the Stickelberger ideal
and the system of independent generators
of the group of circular units of a cyclotomic field,
9. československá konference z teorie čísel, 11.-15.9.1989,
MU SAV, 1989.
[2] R. Kučera, On the bases of the Stickelberger ideal
and the group of circular units of a cyclotomic field,
Algebraische Zahlentheorie, August 12-18,
Mathematisches forschungsinstitut Oberwolfach 1990.
[3] R. Kučera,
Circular units and class groups of abelian fields,
Comptes rendus de la conférence internationale Maroc-Québec (Mai 2003)
"Théorie des nombres et applications", Université Laval, Québec,
Canada 2004, 130-143.
[4] R. Kučera,
On Minus Conjecture, submitted.
Books
[1] J. Herman, R. Kučera and J. Šimša,
Equations and Inequalities: Elementary Problems and Theorems in
Algebra and Number Theory, Canadian Mathematical Society Books in
Mathematics 1, Springer-Verlag, New York 2000.
[2] J. Herman, R. Kučera and J. Šimša,
Counting and Configurations: Problems in Combinatorics, Arithmetic, and
Geometry, Canadian Mathematical Society Books in
Mathematics 12, Springer-Verlag, New York 2003.
Textbooks in Czech
[1] J. Herman, R. Kučera a J. Šimša,
Metody řešení matematických úloh I,
skriptum PřF MU, 334 stran, SPN, Praha 1990, druhé upravené vydání,
skriptum PřF MU, 278 stran, MU, Brno 1996, dotisk 2001.
[2] J. Herman, R. Kučera a J. Šimša,
Metody řešení matematických úloh II,
skriptum PřF MU, 440 stran, MU, Brno 1991, druhé upravené vydání,
skriptum PřF MU, 354 stran, MU, Brno 1997, třetí vydání skriptum PřF MU, 356
stran, MU, Brno 2004.
[3] J. Herman, R. Kučera a J. Šimša,
Seminář ze středoškolské matematiky,
skriptum PřF MU, 36 stran, MU, Brno 1994, dotisk 1998, druhé upravené
vydání, skriptum PřF MU, 51 stran.
[4] R. Kučera a L. Skula, Číselné obory, skriptum PřF MU,
96 stran, MU, Brno 1998.
Electronic Textbooks in Czech
[1] R. Kučera,
Algoritmy teorie čísel, 62 pp.
[2] R. Kučera,
Teorie čísel, 80 pp.
[3] R. Kučera,
Základy teorie svazů, 30 pp.
[4] R. Kučera,
Základy univerzální algebry, 43 pp.