Covering systems, Kubert identities and difference equations

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1. 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). (1951) Zbl0043.07103MR0043843
2. 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. (1953) Zbl0051.30303
3. 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. (1978) 
4. BEEBEE J., Some trigonometric identities related to exact covers, Proc. Amer. Math. Soc. 112 (1991), 329-338. (1991) Zbl0725.11008MR1049133
5. BEEBEE J., Bernoulli numbers and exact covering systems, Amer. Math. Monthly 99 (1992), 946-948. (1992) Zbl0776.11008MR1190561
6. BEEBEE J., Exact covering systems and the Gauß-Legendre multiplication formula for the Gamma function, Proc. Amer. Math. Soc. 120 (1994), 1061-1065. (1994) Zbl0801.11005MR1180463
7. BEEBEE J., Exact covers and the Kubert identities, Manuscript 1995, Department of Mathematical Sciences, University of Alaska Anchorage. Anchorage AK 99508. (1995) 
8. CARLITZ L., The multiplication formulas for the Bernoulli and Euler polynomials, Math. Mag. 27 (1953), 59-64. (1953) Zbl0051.30704MR0058020
9. DEEBA E. Y.-RODRIGUES D. M., Stirling's series and Bernoulli numbers, Amer. Math. Monthly 98 (1991), 423-426. (1991) Zbl0743.11012MR1104307
10. 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. (1990) Zbl0746.11013MR1119305
11. EULER L., Introductio in analysin infinitorum I, Bousquet & Socios., Lausanne, 1748. 
12. EULER L., Institutiones calculi differentialis, Petrograd, 1755. 
13. FRAENKEL A. S., A characterization of exactly covering congruences, Discrete Math. 4 (1973), 359-366. (1973) Zbl0257.10003MR0316359
14. FRAENKEL A. S., Further characterizations and properties of exactly covering congruences, Discrete Math. 12 (1975), 93-100. (1975) Zbl0306.10002MR0374076
15. FROBENIUS G., Über die Bernoulli'schen Zahlen und die Euler'schen Polynome, Sitzungsber. Preuss. Akad. Wiss. (1910), 809-847. (1910) 
16. HURWITZ A., Einige Eigenschaften der Dirichlet’schen Functionen $F\left(s\right)=\Sigma (D/n)·1/n^s$, die bei der Bestimmung der Classenanzahl binarer quadratischer Formen auftreten, Z. Math. Phys. 27 (1882), 86-101. 
17. KOREC I., Irreducible disjoint covering systems, Acta Arit. 44 (1984), 389-395. (1984) Zbl0519.10002MR0777015
18. LANG S., Cyclotomic Fields, Springer Verlag, New York-Heidelberg-Berlin, 1978. (1978) Zbl0395.12005MR0485768
19. LERCH M., Note sur la fonction $\frac{k}{}(w,x,s)={\sum }_{k=0}^{\infty }\frac{g^{2k\pi ix}}{{(w+s)}^x}$, Acta Math. 11 (1887-88), 19-24. MR1554747
20. LERCH M., Foundation of the theory of Malmsten's series, C. R. Czech Acad. Sci. Prague 1 (1892), 1-68. (Czech) 
21. 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) 
22. 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) 
23. LINDELÖF E., Le calcul des résidues et ses applications a la theorie des fonctions, Gauthier-Villars, Paris, 1905. (1905) 
24. LIPSCHITZ R., Untersuchung einer aus vier Elementen gebildeten Reihe, J. Reine Angew. Math. 54 (1857), 313-328. 
25. MALMSTEN, C J., De integralibus quisbusdam definitis, seriebusque infinitis, J. Reine Angew. Math. 38 (1849), 1-39. 
26. MILNOR J., On polylogarithms, Hurwitz zeta functions, and the Kubert identities, Enseign. Math. (2) 29 (1983), 281-322. (1983) Zbl0557.10031MR0719313
27. NIELSEN N., Traité Élémentaire des Nombres de Bernoulli, Gauthier-Villars, Paris, 1923. (1923) 
28. NOVÁK B.-ZNÁM Š., Disjoint covering systems, Amer. Math. Monthly 81 (1974), 42-45. (1974) Zbl0279.10043MR0332632
29. NÖRLUND N. E., Vorlesungen über Differenzenrechnung, Springer Verlag, Berlin, 1924. (1924) 
30. NÖRLUND N. E., Sur la 'Somme' ďune Fonction, Gauthier-Villars, Paris, 1927. (1927) 
31. PORUBSKÝ Š., Natural exactly covering systems of congruences, Czechoslovak Math. J. 99 (1974), 598-606. (1974) Zbl0327.10005MR0354520
32. PORUBSKY Š., Covering systems and generating functions, Acta Arith. 26 (1975), 223-231. (1975) Zbl0268.10044MR0379423
33. PORUBSKÝ Š., On m times covering systems of congruences, Acta Arith. 29 (1976), 159-169. (1976) Zbl0282.10033MR0399033
34. PORUBSKÝ Š., Results and problems on covering systems of residue classes, Mitt. Math. Sem. Giessen 150 (1981). (1981) Zbl0479.10032MR0638657
35. PORUBSKÝ Š., A characterization of finite unions of arithmetic sequences, Discrete Math. 38 (1982), 73-77. (1982) Zbl0474.05001MR0676521
36. PORUBSKÝ Š., Identities involving covering systems I, Math. Slovaca 44 (1994), 153-162. (1994) Zbl0809.11012MR1282532
37. PORUBSKÝ Š., Identities involving covering systems II, Math. Slovaca 44 (1994), 555-568. (1994) Zbl0821.11008MR1338428
38. 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. (1997) MR1689520
39. RAABE J. L., Die Jacob Bernoull'ische Function, Zürich, 1848, pp. 23-28. 
40. STEIN S. K., Unions of arithmetic sequences, Math. Ann. 134 (1958), 289-294. (1958) Zbl0084.04302MR0093493
41. SUN Z., Systems of congruences with multiplicators, (English summary), J. Nanjing Univ. Math. Biq. 6 (1989), 124-133. (Chinese) (1989) Zbl0703.11002MR1027346
42. SUN Z., Several results on systems of residue classes, (Research announcement), Adv. in Math. (China) 18 (1989), 251-252. (1989) 
43. WALUM H., Multiplication formulae for periodic functions, Pacific J. Math. 149 (1991), 383-396. (1991) Zbl0736.11012MR1105705
44. ZNÁM Š., A simple characterization of disjoint covering systems, Discrete Math. 12 (1975), 89-91. (1975) Zbl0306.10001MR0376597