Weighted relationship theorems and Ramanujan expansions
Lutz Lucht
Acta Arithmetica, Tome 69 (1995), p. 25-42 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:206735 
@article{bwmeta1.element.bwnjournal-article-aav70i1p25bwm,
     author = {Lutz Lucht},
     title = {Weighted relationship theorems and Ramanujan expansions},
     journal = {Acta Arithmetica},
     volume = {69},
     year = {1995},
     pages = {25-42},
     zbl = {0818.11005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav70i1p25bwm}
}

Lutz Lucht. Weighted relationship theorems and Ramanujan expansions. Acta Arithmetica, Tome 69 (1995) pp. 25-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav70i1p25bwm/

[000] [1] R. D. Carmichael, Expansions of arithmetical functions in infinite series, Proc. London Math. Soc. (2) 34 (1932), 1-26. | Zbl 0004.29305

[001] [2] E. Cohen, Almost even functions of finite abelian groups, Acta Arith. 7 (1962), 311-323. | Zbl 0114.26503

[002] [3] H. Delange, Sur les fonctions arithmétiques multiplicatives, Ann. Sci. École Norm. Sup. 78 (1961), 273-304. | Zbl 0234.10043

[003] [4] P. D. T. A. Elliott, A mean value theorem for multiplicative functions, Proc. London Math. Soc. (3) 3 (1975), 418-438. | Zbl 0319.10055

[004] [5] G. Halász, Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hungar. 19 (1968), 365-403. | Zbl 0165.05804

[005] [6] G. H. Hardy, Note on Ramanujan’s trigonometrical function cq(n) and certain series of arithmetical functions, Proc. Cambridge Philos. Soc. 20 (1921), 263-271. | Zbl 48.0151.04

[006] [7] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Univ. Press, London, 1960. | Zbl 0086.25803

[007] [8] E. Heppner und W. Schwarz, Benachbarte multiplikative Funktionen, in: Studies in Pure Mathematics (To the Memory of Paul Turán), Budapest, 1983, 323-336. | Zbl 0518.10050

[008] [9] J. Knopfmacher, Abstract Analytic Number Theory, Dover, New York, 1975 (1990). | Zbl 0743.11002

[009] [10] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, 2nd ed. reprint., Chelsea, New York, 1953. | Zbl 0051.28007

[010] [11] L. Lucht, An application of Banach algebra techniques to multiplicative functions, Math. Z. 214 (1993), 287-295. | Zbl 0805.11067

[011] [12] S. Ramanujan, On certain trigonometrical sums and their applications in the theory of numbers, Trans. Cambridge Philos. Soc. 22 (1918), 259-276; Collected Papers, Cambridge, 1927, No. 21.

[012] [13] W. Rudin, Real and Complex Analysis, McGraw-Hill, London, 1970.

[013] [14] W. Schwarz, Ramanujan-Entwicklungen stark multiplikativer zahlentheoretischer Funktionen, Acta Arith. 22 (1973), 329-338. | Zbl 0222.10007

[014] [15] W. Schwarz, Ramanujan-Entwicklung stark multiplikativer Funktionen, J. Reine Angew. Math. 262//263 (1973), 66-73.

[015] [16] W. Schwarz, Über die Ramanujan-Entwicklung multiplikativer Funktionen, Acta Arith. 27 (1975), 269-279. | Zbl 0267.10061

[016] [17] W. Schwarz, Fourier-Ramanujan-Entwicklungen zahlentheoretischer Funktionen und Anwendungen, Festschrift J. W. Goethe-Universität, Frankfurt//Main (1981), 399-415. | Zbl 0459.10034

[017] [18] W. Schwarz und J. Spilker, Eine Anwendung des Approximationssatzes von Weierstrass-Stone auf Ramanujan-Summen, Nieuw Arch. Wisk. (3) 19 (1971), 198-209.

[018] [19] W. Schwarz und J. Spilker, Arithmetical Functions, Cambridge University Press, Cambridge, 1994. | Zbl 0807.11001

[019] [20] F. Tuttas, Über die Entwicklung multiplikativer Funktionen nach Ramanujan-Summen, Acta Arith. 36 (1980), 257-270. | Zbl 0433.10032

[020] [21] R. Warlimont, Ramanujan expansions of multiplicative functions, Acta Arith. 42 (1983), 111-120. | Zbl 0462.10031

[021] [22] A. Wintner, Eratosthenian Averages, Waverly, Baltimore, 1944