| Title:
|
Covering systems, Kubert identities and difference equations (English) |
| Author:
|
Porubský, Štefan |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
381-413 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11B25 |
| MSC:
|
11B68 |
| MSC:
|
11B83 |
| MSC:
|
11M35 |
| MSC:
|
33B15 |
| MSC:
|
39A05 |
| idZBL:
|
Zbl 0991.11005 |
| idMR:
|
MR1857297 |
| . |
| Date available:
|
2009-09-25T11:46:16Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/136785 |
| . |
| Reference:
|
[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). Zbl 0043.07103, MR 0043843 |
| Reference:
|
[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 0051.30303 |
| Reference:
|
[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. |
| Reference:
|
[Beeb1991] BEEBEE J.: Some trigonometric identities related to exact covers.Proc. Amer. Math. Soc. 112 (1991), 329-338. Zbl 0725.11008, MR 1049133 |
| Reference:
|
[Beeb1992] BEEBEE J.: Bernoulli numbers and exact covering systems.Amer. Math. Monthly 99 (1992), 946-948. Zbl 0776.11008, MR 1190561 |
| Reference:
|
[Beeb1994] BEEBEE J.: Exact covering systems and the Gauß-Legendre multiplication formula for the Gamma function.Proc. Amer. Math. Soc. 120 (1994), 1061-1065. Zbl 0801.11005, MR 1180463 |
| Reference:
|
[Beeb1995] BEEBEE J.: Exact covers and the Kubert identities.Manuscript 1995, Department of Mathematical Sciences, University of Alaska Anchorage. Anchorage AK 99508. |
| Reference:
|
[Carl1953] CARLITZ L.: The multiplication formulas for the Bernoulli and Euler polynomials.Math. Mag. 27 (1953), 59-64. Zbl 0051.30704, MR 0058020 |
| Reference:
|
[DeRo1991] DEEBA E. Y.-RODRIGUES D. M.: Stirling's series and Bernoulli numbers.Amer. Math. Monthly 98 (1991), 423-426. Zbl 0743.11012, MR 1104307 |
| Reference:
|
[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. Zbl 0746.11013, MR 1119305 |
| Reference:
|
[Eule1748] EULER L.: Introductio in analysin infinitorum I.Bousquet & Socios., Lausanne, 1748. |
| Reference:
|
[Eule1755] EULER L.: Institutiones calculi differentialis.Petrograd, 1755. |
| Reference:
|
[Frae1973] FRAENKEL A. S.: A characterization of exactly covering congruences.Discrete Math. 4 (1973), 359-366. Zbl 0257.10003, MR 0316359 |
| Reference:
|
[Frae1975] FRAENKEL A. S.: Further characterizations and properties of exactly covering congruences.Discrete Math. 12 (1975), 93-100. Zbl 0306.10002, MR 0374076 |
| Reference:
|
[Frob1910] FROBENIUS G.: Über die Bernoulli'schen Zahlen und die Euler'schen Polynome.Sitzungsber. Preuss. Akad. Wiss. (1910), 809-847. |
| Reference:
|
[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. |
| Reference:
|
[Kore1984] KOREC I.: Irreducible disjoint covering systems.Acta Arit. 44 (1984), 389-395. Zbl 0519.10002, MR 0777015 |
| Reference:
|
[Lang1978] LANG S.: Cyclotomic Fields.Springer Verlag, New York-Heidelberg-Berlin, 1978. Zbl 0395.12005, MR 0485768 |
| Reference:
|
[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 1554747 |
| Reference:
|
[Lerc1892] LERCH M.: Foundation of the theory of Malmsten's series.C. R. Czech Acad. Sci. Prague 1 (1892), 1-68. (Czech) |
| Reference:
|
[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) |
| Reference:
|
[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) |
| Reference:
|
[Lind1905] LINDELÖF E.: Le calcul des résidues et ses applications a la theorie des fonctions.Gauthier-Villars, Paris, 1905. |
| Reference:
|
[Lips1857] LIPSCHITZ R.: Untersuchung einer aus vier Elementen gebildeten Reihe.J. Reine Angew. Math. 54 (1857), 313-328. |
| Reference:
|
[Malm1849] MALMSTEN, C J.: De integralibus quisbusdam definitis, seriebusque infinitis.J. Reine Angew. Math. 38 (1849), 1-39. |
| Reference:
|
[Miln1983] MILNOR J.: On polylogarithms, Hurwitz zeta functions, and the Kubert identities.Enseign. Math. (2) 29 (1983), 281-322. Zbl 0557.10031, MR 0719313 |
| Reference:
|
[Niel1923] NIELSEN N.: Traité Élémentaire des Nombres de Bernoulli.Gauthier-Villars, Paris, 1923. |
| Reference:
|
[NoZn1974] NOVÁK B.-ZNÁM Š.: Disjoint covering systems.Amer. Math. Monthly 81 (1974), 42-45. Zbl 0279.10043, MR 0332632 |
| Reference:
|
[Nörl1924] NÖRLUND N. E.: Vorlesungen über Differenzenrechnung.Springer Verlag, Berlin, 1924. |
| Reference:
|
[Nörl1927] NÖRLUND N. E.: Sur la 'Somme' ďune Fonction.Gauthier-Villars, Paris, 1927. |
| Reference:
|
[Poru1974] PORUBSKÝ Š.: Natural exactly covering systems of congruences.Czechoslovak Math. J. 99 (1974), 598-606. Zbl 0327.10005, MR 0354520 |
| Reference:
|
[Poru1975] PORUBSKY Š.: Covering systems and generating functions.Acta Arith. 26 (1975), 223-231. Zbl 0268.10044, MR 0379423 |
| Reference:
|
[Poru1976] PORUBSKÝ Š.: On m times covering systems of congruences.Acta Arith. 29 (1976), 159-169. Zbl 0282.10033, MR 0399033 |
| Reference:
|
[Poru1981] PORUBSKÝ Š.: Results and problems on covering systems of residue classes.Mitt. Math. Sem. Giessen 150 (1981). Zbl 0479.10032, MR 0638657 |
| Reference:
|
[Poru1982] PORUBSKÝ Š.: A characterization of finite unions of arithmetic sequences.Discrete Math. 38 (1982), 73-77. Zbl 0474.05001, MR 0676521 |
| Reference:
|
[Por1994a] PORUBSKÝ Š.: Identities involving covering systems I.Math. Slovaca 44 (1994), 153-162. Zbl 0809.11012, MR 1282532 |
| Reference:
|
[Por1994b] PORUBSKÝ Š.: Identities involving covering systems II.Math. Slovaca 44 (1994), 555-568. Zbl 0821.11008, MR 1338428 |
| Reference:
|
[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 1689520 |
| Reference:
|
[Raab1848] RAABE J. L.: Die Jacob Bernoull'ische Function.Zürich, 1848, pp. 23-28. |
| Reference:
|
[Stei1958] STEIN S. K.: Unions of arithmetic sequences.Math. Ann. 134 (1958), 289-294. Zbl 0084.04302, MR 0093493 |
| Reference:
|
[Sun1989a] SUN Z.: Systems of congruences with multiplicators.(English summary), J. Nanjing Univ. Math. Biq. 6 (1989), 124-133. (Chinese) Zbl 0703.11002, MR 1027346 |
| Reference:
|
[Sun1989b] SUN Z.: Several results on systems of residue classes.(Research announcement), Adv. in Math. (China) 18 (1989), 251-252. |
| Reference:
|
[Walu1991] WALUM H.: Multiplication formulae for periodic functions.Pacific J. Math. 149 (1991), 383-396. Zbl 0736.11012, MR 1105705 |
| Reference:
|
[Znám1975] ZNÁM Š.: A simple characterization of disjoint covering systems.Discrete Math. 12 (1975), 89-91. Zbl 0306.10001, MR 0376597 |
| . |
