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List of important references


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\bibitem [B]{B}
{\sf BARONE, H.G.:}
\textit{Limit points of sequences and their
transforms by methods of summability},
Duke Math. J.
\textbf{5} (1939), 740--752 (Zbl 0022.21902).
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\bibitem[2]{2}
{\sf BILLINGSLEY, P.:}
\textsl{Convergence of Probability Measures},
John Wiley \& Sons Inc,
New~York, 1968.
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\bibitem [Buc]{BUC}
{\sf BUCK, R.C.:}
\textit{The measure theoretic approach to density},
 Amer. J. Math.
\textbf{68}  (1946),  560--580.
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\bibitem[Da33]{D}
{\sf DAVENPORT, H.:}
\textit{Uber numeri abundantes}, Sitzungsber.
Preuss. Acad., Phys.-Math. Kl.
\textbf{27} (1933), 830--837.
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\bibitem[Da80]{Da}
{\sf DAVENPORT, H.:}
\textsl{Multiplicative Number Theory},
Second edition, Grad. Text in Math. Vol. {\bf 74},
Springer-Verlag,
Berlin, 1980.
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\bibitem [DT97]{DT}
{\sf DRMOTA, M.--TICHY, R. F.:}
\textsl {Sequences, Discrepancies and Applications},
Lecture Notes in Mathematics \textbf{1651},
Springer-Verlag,
Berlin, Heidelberg, 1997.
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\bibitem [E1]{E1}
{\sf ELLIOT, P.D.T.A.:}
\textsl{Probabilistic Number Theory I (Mean-Value Theorems)},
Springer-Verlag,
New York, Heidelberg, Berlin, 1979.
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\bibitem [E1]{E1}
{\sf ELLIOT, P.D.T.A.:}
\textsl{Probabilistic Number Theory II (Central Limit Theorems)},
Springer-Verlag,
New York, Heidelberg, Berlin, 1980.
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\bibitem[E39]{E1}
{\sf ERD\H{O}S, P.:}
\textsl{On the smoothness of the asymptotic
distribution of additive arithmetical functions},
Amer. J. Math.
\textbf{61} (1939), 722--725.
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\bibitem[E46]{E2}
{\sf ERD\H{O}S, P.:}
\textit{Some remarks about additive and
multiplicative functions},
Bull. Amer. Mat. Soc.
\textbf{52} (1946), 527--537.
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\bibitem[E74]{E3}
{\sf ERD\H{O}S, P.:}
\textit{On the distribution of numbers of the
form $\sigma(n)/n$ and some related questions},
Pacific Jour. Math.
\textbf{52} (1974), 59--65.
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\bibitem[F67]{F}
{\sf FA\v INLE\v IB, A.S.:}
\textit{On the distribution of values of
Euler's function}, (Russian)
Mat. zametki
\textbf{1} (1967), no. 6, 645--652.
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\bibitem[Gr]{Gr}
{\sf GRAVES, G.:}
\textsl{Sieves in Number Theory},
Springer-Verlag,
Berlin,  2001.
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\bibitem[HR]{HR}
{\sf HALBERSTAM, H. -- RICHTER, H.-E.:}
\textsl{Sieve Methods},
London Mathematical Society Monographs No. \textbf{4},
Academic Press,
London, New York, 1974.
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\bibitem[HW]{HaWr}
{\sf HARDY, G.H. -- WRIGHT, E.M.}
\textsl{An Introduction to the Theory of Numbers}, Third edition,
Oxford at the Clarendon Press,
Oxford, 1979.
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\bibitem[Hl]{Hla3}
{\sf HLAWKA, E.:}
\textit{Zur formalen Theorie der Gleichverteilung
in kompakten Gruppen},
Rend. Circ. Mat. Palermo
(2)\textbf{4} (1955), 33--47 (MR \textbf{17}, 594c).
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\bibitem[Hl1]{Hla1}
{\sf HLAWKA, E.:}
\textit{Funktionen von beschr\"ankter Variation in
der Theorie der Gleichverteilung},
Ann. Mat. Pura Appl.
(4)\textbf{54} (1961), 325--333.
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\bibitem[Hl2]{H2}
{\sf HLAWKA, E.:}
\textit{Zur angen\"aherten Berechnung mehrfacher Integrale},
Monatsh. Math.
\textbf{66} (1962), 140--151.
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\bibitem[Hl3]{H3}
{\sf HLAWKA, E.:}
\textsl{Theorie der Gleichverteilung},
Bibl. Institut, Mannheim, Wien, Zürich,
1979 (MR 80j:10057) (English translation 1984).
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\bibitem[Iv]{Iv}
{\sf IVI\'C, A.:}
\textsl{The Riemann Zeta-Function},
Wiley-Interscience,
New York, 1985.
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\bibitem[Kh]{KH}
{\sf KHINTCHINE, A.:}
\textit{Einige S\"atze \"uber Kettenbr\"uche,
mit Anwendungen auf die Theorie der
Diophantischen Approximationen},
Math. Ann.
\textbf{92} (1924), 115--125.
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\bibitem[Kn1]{K1}
{\sf KNESER, M.:}
\textit{Absch\"atzung der asymptotischen Dichte von
Summenmengen},
Math. Z.
\textbf{58} (1953), 459--484.
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\bibitem[Kn2]{K2}
{\sf KNESER, M.:}
\textit{Ein Satz \"uber abelsche Gruppen mit
Anwendungen auf die Geometrie der Zahlen},
Math. Z.
\textbf{61} (1955), 429--434.
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\bibitem [K1]{K}
{\sf KNUTH, D.E.:}
\textsl{Seminumerical Algorithms. The Art of
Computer Programming, Vol 2, 2nd},
Addison Wesley,
Reading, MA, 1981.
(First ed.: Reading, MA, 1969 (MR \textbf{44}\#3531))
Russian translation Izd. Mir,
Moscow, 1977.
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\bibitem[K2]{K1}
{\sf KOKSMA, J.F.:}
\textit{Asymptotische verdeling van getallen
modulo 1. I,II,III},
Mathematica (Leiden)
\textbf{1} (1933), 245--248;
\textbf{2} (1933), 1--6, 107--114 (Zbl 0007.33901).
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\bibitem[K3]{K3}
{\sf KOKSMA, J.F.:}
\textsl{Diophantische Approximationen},
Ergebnisse der Mathematik und Ihrer Grenzgebiete \textbf{4},
Julius Springer,
Berlin, 1936 (Zbl 0012.39602).
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\bibitem[Ko1]{Ko1}
{\sf KOKSMA, J.F.:}
\textit{A general theorem from the theory of
uniform distribution modulo 1} (Dutch),
Mathematica, Zutphen. B.
\textbf{11} (1942), 7--11.
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\bibitem[Ko2]{Ko2}
{\sf KOKSMA, J.F.:}
\textsl{Some Theorems on Diophantine
Inequalities},
Scriptum no. \textbf{5},
Math. Centrum Amsterdam,
1950, 51 pp.
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\bibitem{Kor}
{\sf KOROBOV, N.M.:}
\textit{Approximate calculation of repeated
integrals by number-theoretical methods} (Russian),
Dokl. Akad. Nauk SSSR (N.S.)
\textbf{115} (1957), 1062--1065.
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\bibitem [KN74]{KN}
{\sf KUIPERS, L.-- NIEDERREITER, H.:}
\textsl{Uniform Distribution of Sequences},
John Wiley \& Sons,
New York, 1974
(Reprint edition in Dover Publications, Inc. Mineola,
New York, 2006).
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\bibitem[L1909]{L}
{\sf LANDAU, E.:}
\textsl{Handbuch der Lehre von der Verteilung der
Primzahlen},
Band 1, Verlag von B.G. Teubner,
Leipzig, 1909.
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\bibitem[La94]{Lang:ANT}
{\sf LANG, S.:}
\textsl{Algebraic Number Theory},
Graduate Texts in Mathematics, Vol. \textbf{110} (second edition),
Springer-Verlag,
New York, 1994.
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\bibitem[Lev]{Lev}
{\sf LEVEQUE,  W.J.:}
\textit{An inequality connected with Weyl's
criterion for uniform distribution}, in:
Proc. Sympos. Pure Math.
Vol. \textbf{VIII}, Amer. Math. Soc.,
Providence, R.I., 1965, pp. 22--30.
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\bibitem[LN83]{LN}
{\sf LIDL, R.  -- NIEDERREITER, H.:}
\textsl{Finite Fields},
Encyclopedia of Mathematics and its Applications \textbf{20},
Addison-Wesley Publishing Company,
Advanced Book Program,
Reading, MA, 1983 (MR0746963).
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\bibitem[LN86]{LN}
{\sf LIDL, R.  -- NIEDERREITER, H.:}
\textsl{Introduction to finite
fields and their applications},
Cambridge University Press,
Cambridge, 1986 (MR0860948);
Second edition: Cambridge University Press,
Cambridge, 1997.
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\bibitem{mat}
{\sf MATOU\v SEK, J.}
\textsl{Geometric Discrepancy},
Algorithms and Combinatorics \textbf{18},
Springer,
Berlin, 1999.
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\bibitem[MSC]{MSC}
{\sf MITRINOVIC, D.S. -- S\'ANDOR, J. -- CRSTICI, B.:}
\textsl{Handbook of Number Theory}
Mathematics and its Applications Vol. \textbf{351},
Kluver Academic Publisher,
Dordrecht, 1996.
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\bibitem[Na74]{Narkiewicz:1974}
{\sf NARKIEWICZ, W.:}
\textsl{Elementary and Analytic Theory of
Algebraic Numbers},
Monografie matematyczne Vol. \textbf{54},
PWN - Polish Scientific Publishers,
Warsaw, 1974.
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\bibitem [Na90]{Na}
{\sf NARKIEWICZ, W.:} \textsl{Number Theory} (Poland),
Biblioteka Matematyczna Tom \textbf{50},
PWN,
Warsaw, 1990.
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\bibitem[Na]{N}
{\sf NATHANSON, M. B.:}
\textsl{Additive Number Theory. Inverse
Problems and the Geometry of Sumsets},
Graduate Texts in Mathematics Vol. \textbf{165},
Springer Verlag, New York, 1996.
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\bibitem [Ni92]{N}
{\sf NIEDERREITER, H.:}
\textsl{Random Number Generation and
Quasi--Monte Carlo Methods},
CBMS--NSF Regional Conference Series in
Applied Mathematics \textbf{63},
Society for Industrial and Applied Mathematics,
Philadelphia, PA, 1992.
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\bibitem[Ph]{plt}
{\sf PHILIPP, W.:}
\textit{Limit theorems for lacunary series and
uniform distribution mod 1},
Acta Arith.
\textbf{26} (1975), 241--251.
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\bibitem[Pe66]{12}
{\sf PETERSEN, G.M.:}
\textsl{Regular Matrix Transformations},
McGraw-Hill Publishing Co., Ltd.,
London, New York, Toronto, Ont., 1966.
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\bibitem[Pey69]{13}
{\sf PEYERIMHOFF, A.:}
\textsl{Lectures on Summability},
Lecture Notes in Mathematics Vol. \textbf{107},
Springer-Verlag,
Berlin, New York, 1969.
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\bibitem [Po71]{Po}
{\sf POSTNIKOV, A. G.:}
\textsl{Introduction to Analytic Number Theory} (Russian),
Izd. Nauka,
Moscow, 1971;
English translation by G. A. Kandall,
Translation of Mathematical Monographs Vol. \textbf{68},
Amer. Math. Soc.,
Providence, RI, 1988.
%%%%%%%%%%%%%%%%%%
\bibitem[Ra76]{Rauzy}
{\sf RAUZY, G.:}
\textsl{Propri\'et\'es statistiques de suites
arithm\'etiques},
Le Math\'ematicien \textbf{15},
Collection SUP, Presses Universitaires de France,
Paris, 1976 ({MR \textbf{53}\#13152}).
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\bibitem[Ri95]{R}
{\sf RIBENBOIM, P.:}
\textsl{The New Book of Prime Number Records},
Springer-Verlag,
New York, 1995.
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\bibitem[Ro]{Ro}
{\sf ROTH,  K.F.:}
\textit{On irregularities of distribution},
Mathematika \textbf{1} (1954), 73--79.
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\bibitem[Sch72]{sch}
{\sf SCHMIDT, W.M.}
\textit{Irregularities of distribution VII},
Acta Arith.
\textbf{21} (1972), 45--50.
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\bibitem[Sch80]{S}
{\sf SCHMIDT, W.M.:}
\textsl{Diophantine Approximation},
Lecture Notes in Math. No. \textbf{785},
Springer-Verlag, Berlin-Heidelberg-New York, 1980.
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\bibitem[SW58]{SW}
{\sf SCHINZEL, A. -- WANG, Y.:}
\textit{A note on some properties of
the functions $\phi(n)$, $\sigma(n)$ and $\theta(n)$},
Ann. Polon. Math.
\textbf{4} (1958), 201--213.
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\bibitem[Sch28]{S1}
{\sf SCHOENBERG, I.J.:}
\textit{\"Uber die asymptotische Verteilung
reeller Zahlen $\mod 1$},
Math. Z.
\textbf{28} (1928), 171--199 (JFM 54.0212.02).
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\bibitem[Sch36]{S2}
{\sf SCHOENBERG, I.J.:}
\textit{On asymptotic distribution of
arithmetical functions},
Trans. Amer. Math. Soc.
\textbf{39} (1936), 315--330.
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\bibitem [SP05]{SP}
{\sf STRAUCH, O. -- PORUBSK\'Y, \v S.:}
\textsl{Distribution of Sequences: A Sampler},
Schriftenreihe der Slowakischen Akademie der
Wissenschaften, Band \textbf{1},
Peter Lang,
Bern-Frankfurt am Main, 2005.
%%%%%%%%%%%%%%%%
\bibitem[Te95]{Tezuka1}
{\sf TEZUKA, S.:}
\textsl{Uniform Random Numbers: Theory and Practice},
Kluwer Academic Publishers,
Dordrecht, 1995.
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\bibitem[vdC]{C}
{\sf VAN DER CORPUT, J.G.:}
\textit{Verteilungsfunktionen. I. Mitt},
Proc. Akad. Wet. Amsterdam
\textbf{38} (1935), 813--821 (Zbl 0012.34705).
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\bibitem[vdC]{C}
{\sf VAN DER CORPUT, J.G.:}
\textit{Verteilungsfunktionen. II},
Proc. Akad. Amsterdam
\textbf{38} (1935), 1058-1066 (JFM 61.0203.01).
%%%%%%%%%%%%%%%%
\bibitem[We14]{W1}
{\sf WEYL, H.:}
\textit{{\"U}ber ein {P}roblem aus dem {G}ebiet der diophantischen
{A}pproximationen},
Nachr. Ges. Wiss. Göttingen, {M}ath.--phys.Kl.
(1914), 234--244 (JFM 45.0325.01).
%%%%%%%%%%%%%%%%
\bibitem[We16]{WE}
{\sf WEYL, H.:}
\textit{\"Uber die Gleichverteilung von Zahlen mod. Eins},
Math. Ann. \textbf{77} (1916), 313--352.
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\bibitem[Z02]{zt}
{\sf ZYGMUND, A.:}
\textsl{Trigonometric Series. Vol. I, II.},
Cambridge Mathematical Library,
Cambridge University Press,
Cambridge, 2002.
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