Covering systems, Kubert identities and difference equations
Mathematica slovaca, Tome 50 (2000) no. 4, pp. 381-413
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11B25, 11B68, 11B83, 11M35, 33B15, 39A05
@article{MASLO_2000_50_4_a2,
     author = {Porubsk\'y, \v{S}tefan},
     title = {Covering systems, {Kubert} identities and difference equations},
     journal = {Mathematica slovaca},
     pages = {381--413},
     year = {2000},
     volume = {50},
     number = {4},
     mrnumber = {1857297},
     zbl = {0991.11005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_2000_50_4_a2/}
}
TY  - JOUR
AU  - Porubský, Štefan
TI  - Covering systems, Kubert identities and difference equations
JO  - Mathematica slovaca
PY  - 2000
SP  - 381
EP  - 413
VL  - 50
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MASLO_2000_50_4_a2/
LA  - en
ID  - MASLO_2000_50_4_a2
ER  - 
%0 Journal Article
%A Porubský, Štefan
%T Covering systems, Kubert identities and difference equations
%J Mathematica slovaca
%D 2000
%P 381-413
%V 50
%N 4
%U http://geodesic.mathdoc.fr/item/MASLO_2000_50_4_a2/
%G en
%F MASLO_2000_50_4_a2
Porubský, Štefan. Covering systems, Kubert identities and difference equations. Mathematica slovaca, Tome 50 (2000) no. 4, pp. 381-413. http://geodesic.mathdoc.fr/item/MASLO_2000_50_4_a2/

[Apos1952] APOSTOL T. M.: On the Lerch zeta function. Pacific J. Math. 1 (1951), 161-167 (Addendum to: On the Lerch zeta function, ibid 2 (1952). 10). | MR | Zbl

[BaEr1953] ERDELYI A.-MAGNUS W.-OBERHETTINGER F.-TRICOMI F. G.: Higher Transcendental Functions. Vol. I. (Bateman Manuscript Project), McGraw-Hill Book Co., New York-London-Toronto, 1953. | Zbl

[Beeb1978] BEEBEE J.: Exact covering systems, cyclic sequences, and circuits in the d-Cube. Manuscript 1978, Department of Mathematical Sciences, University of Alaska Anchorage, Anchorage AK 99508.

[Beeb1991] BEEBEE J.: Some trigonometric identities related to exact covers. Proc. Amer. Math. Soc. 112 (1991), 329-338. | MR | Zbl

[Beeb1992] BEEBEE J.: Bernoulli numbers and exact covering systems. Amer. Math. Monthly 99 (1992), 946-948. | MR | Zbl

[Beeb1994] BEEBEE J.: Exact covering systems and the Gauß-Legendre multiplication formula for the Gamma function. Proc. Amer. Math. Soc. 120 (1994), 1061-1065. | MR | Zbl

[Beeb1995] BEEBEE J.: Exact covers and the Kubert identities. Manuscript 1995, Department of Mathematical Sciences, University of Alaska Anchorage. Anchorage AK 99508.

[Carl1953] CARLITZ L.: The multiplication formulas for the Bernoulli and Euler polynomials. Math. Mag. 27 (1953), 59-64. | MR | Zbl

[DeRo1991] DEEBA E. Y.-RODRIGUES D. M.: Stirling's series and Bernoulli numbers. Amer. Math. Monthly 98 (1991), 423-426. | MR | Zbl

[DiSS1991] Bernoulli Numbers. (Bibliography 1713-1990) (Dilcher, K., Skula, L., Slavutskij, I. Sh., eds.) Queen's Papers in Pure and Appl. Math. 87, Queen's Univ., Kingston, ON, 1991. | MR | Zbl

[Eule1748] EULER L.: Introductio in analysin infinitorum I. Bousquet & Socios., Lausanne, 1748.

[Eule1755] EULER L.: Institutiones calculi differentialis. Petrograd, 1755.

[Frae1973] FRAENKEL A. S.: A characterization of exactly covering congruences. Discrete Math. 4 (1973), 359-366. | MR | Zbl

[Frae1975] FRAENKEL A. S.: Further characterizations and properties of exactly covering congruences. Discrete Math. 12 (1975), 93-100. | MR | Zbl

[Frob1910] FROBENIUS G.: Über die Bernoulli'schen Zahlen und die Euler'schen Polynome. Sitzungsber. Preuss. Akad. Wiss. (1910), 809-847.

[Hurw1882] HURWITZ A.: Einige Eigenschaften der Dirichlet'schen Functionen $F(s) = Σ(D/n)\cdot 1/n^s$, die bei der Bestimmung der Classenanzahl binarer quadratischer Formen auftreten. Z. Math. Phys. 27 (1882), 86-101.

[Kore1984] KOREC I.: Irreducible disjoint covering systems. Acta Arit. 44 (1984), 389-395. | MR | Zbl

[Lang1978] LANG S.: Cyclotomic Fields. Springer Verlag, New York-Heidelberg-Berlin, 1978. | MR | Zbl

[Lerc1887] LERCH M.: Note sur la fonction ${\frac k}(w,x,s) = \sum_{k=0}^\infty \frac{g^{2k\pi i x}}{(w+s)^x}$. Acta Math. 11 (1887-88), 19-24. | MR

[Lerc1892] LERCH M.: Foundation of the theory of Malmsten's series. C. R. Czech Acad. Sci. Prague 1 (1892), 1-68. (Czech)

[Lerc1893] LERCH M.: Investigations in the theory of Malmsten's series and invariants of quadratic forms. C R. Czech Acad. Sci. Prague 2 (1893), 1-11. (Czech)

[Lerc1894] LERCH M.: Further investigation of Malmsten's series. C. R. Czech Acad. Sci. Prague 3 (1894), 1-61 (cf. Jahrbuch Über die Fortschritte der Math. 25 (1893-94), p. 484). (Czech)

[Lind1905] LINDELÖF E.: Le calcul des résidues et ses applications a la theorie des fonctions. Gauthier-Villars, Paris, 1905.

[Lips1857] LIPSCHITZ R.: Untersuchung einer aus vier Elementen gebildeten Reihe. J. Reine Angew. Math. 54 (1857), 313-328.

[Malm1849] MALMSTEN, C J.: De integralibus quisbusdam definitis, seriebusque infinitis. J. Reine Angew. Math. 38 (1849), 1-39.

[Miln1983] MILNOR J.: On polylogarithms, Hurwitz zeta functions, and the Kubert identities. Enseign. Math. (2) 29 (1983), 281-322. | MR | Zbl

[Niel1923] NIELSEN N.: Traité Élémentaire des Nombres de Bernoulli. Gauthier-Villars, Paris, 1923.

[NoZn1974] NOVÁK B.-ZNÁM Š.: Disjoint covering systems. Amer. Math. Monthly 81 (1974), 42-45. | MR | Zbl

[Nörl1924] NÖRLUND N. E.: Vorlesungen über Differenzenrechnung. Springer Verlag, Berlin, 1924.

[Nörl1927] NÖRLUND N. E.: Sur la 'Somme' ďune Fonction. Gauthier-Villars, Paris, 1927.

[Poru1974] PORUBSKÝ Š.: Natural exactly covering systems of congruences. Czechoslovak Math. J. 99 (1974), 598-606. | MR | Zbl

[Poru1975] PORUBSKY Š.: Covering systems and generating functions. Acta Arith. 26 (1975), 223-231. | MR | Zbl

[Poru1976] PORUBSKÝ Š.: On m times covering systems of congruences. Acta Arith. 29 (1976), 159-169. | MR | Zbl

[Poru1981] PORUBSKÝ Š.: Results and problems on covering systems of residue classes. Mitt. Math. Sem. Giessen 150 (1981). | MR | Zbl

[Poru1982] PORUBSKÝ Š.: A characterization of finite unions of arithmetic sequences. Discrete Math. 38 (1982), 73-77. | MR | Zbl

[Por1994a] PORUBSKÝ Š.: Identities involving covering systems I. Math. Slovaca 44 (1994), 153-162. | MR | Zbl

[Por1994b] PORUBSKÝ Š.: Identities involving covering systems II. Math. Slovaca 44 (1994), 555-568. | MR | Zbl

[Por1999] PORUBSKÝ Š.: Identities with covering systems and Appell polynomials. In: Number Theory in Progress. Procedings of the International conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the б0th Birthday of Andrzej Schinzel, Zakopane 1997, Walter de Gruyter, Berlin-New York, 1999, pp. 407-417. | MR

[Raab1848] RAABE J. L.: Die Jacob Bernoull'ische Function. Zürich, 1848, pp. 23-28.

[Stei1958] STEIN S. K.: Unions of arithmetic sequences. Math. Ann. 134 (1958), 289-294. | MR | Zbl

[Sun1989a] SUN Z.: Systems of congruences with multiplicators. (English summary), J. Nanjing Univ. Math. Biq. 6 (1989), 124-133. (Chinese) | MR | Zbl

[Sun1989b] SUN Z.: Several results on systems of residue classes. (Research announcement), Adv. in Math. (China) 18 (1989), 251-252.

[Walu1991] WALUM H.: Multiplication formulae for periodic functions. Pacific J. Math. 149 (1991), 383-396. | MR | Zbl

[Znám1975] ZNÁM Š.: A simple characterization of disjoint covering systems. Discrete Math. 12 (1975), 89-91. | MR | Zbl