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1992 | 61 | 3 | 209-225
Tytuł artykułu

Hans Rademacher (1892-1969)

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
61
Numer
3
Strony
209-225
Opis fizyczny
Daty
wydano
1992
otrzymano
1992-01-03
Twórcy
  • Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801, U.S.A.
Bibliografia
  • [1] L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938), 359-364.
  • [2] G. E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976.
  • [3] A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J. 8 (1967), 67-78.
  • [4] B. C. Berndt, Generalized Dedekind eta-functions and generalized Dedekind sums, Trans. Amer. Math. Soc. 178 (1973), 495-508.
  • [5] B. C. Berndt, Generalized Eisenstein series and modified Dedekind sums, J. Reine Angew. Math. 272 (1975), 182-193.
  • [6] B. C. Berndt, Reciprocity theorems for Dedekind sums and generalizations, Adv. in Math. 23 (1977), 285-316.
  • [7] B. C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan, J. Reine Angew. Math. 304 (1978), 332-365.
  • [8] R. W. Bruggeman, Dedekind sums and Fourier coefficients of modular forms, J. Number Theory 36 (1990), 289-321.
  • [9] Y. Chuman, Generators and relations of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 381-390.
  • [10] H. Davenport, Multiplicative Number Theory, 2nd ed., Springer, New York 1980.
  • [11] R. Dedekind, Erläuterungen zu zwei Fragmenten von Riemann, in: Gesammelte Mathematische Werke, Friedr. Vieweg & Sohn, Braunschweig 1930, 159-172.
  • [12] H. Frasch, Die Erzeugenden der Hauptkongruenzgruppen für Primzahlstufen, Math. Ann. 108 (1933), 229-252.
  • [13] L. A. Goldberg, Transformations of Theta-functions and Analogues of Dedekind Sums, Ph.D. Dissertation, University of Illinois at Urbana-Champaign, 1981.
  • [14] E. Grosswald, On the structure of some subgroups of the modular group, Amer. J. Math. 72 (1950), 809-834.
  • [15] E. Grosswald, On the parabolic generators of the principal congruence subgroups of the modular group, Amer. J. Math. 74 (1952), 435-443.
  • [16] E. Grosswald, An orthonormal system and its Lebesgue constants, in: Analytic Number Theory, M. I. Knopp (ed.), Lecture Notes in Math. 899, Springer, Berlin 1981, 2-9.
  • [17] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, New York 1974.
  • [18] G. H. Hardy, Collected Papers, Vol. 1, Clarendon Press, Oxford 1966.
  • [19] G. H. Hardy and J. E. Littlewood, Some problems of Diophantine approximation. I. The fractional part of $n^{k}θ$, Acta Math. 37 (1914), 155-191.
  • [20] G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio Numerorum'; III: On the expression of a number as a sum of primes, Acta Math. 44 (1922), 1-70.
  • [21] G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. (2) 17 (1918), 75-115.
  • [22] E. Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen. Zweite Mitteilung, Math. Z. 6 (1920), 11-51.
  • [23] E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktenwicklung. I, Math. Ann. 114 (1937), 1-28.
  • [24] E. Hecke, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen 1970.
  • [25] D. R. Hickerson, Continued fractions and density results for Dedekind sums, J. Reine Angew. Math. 290 (1977), 113-116.
  • [26] F. John, Identitäten zwischen dem Integral einer willkürlichen Funktion und unendlichen Reihen, Math. Ann. 110 (1935), 718-721.
  • [27] M. Knopp, Modular Functions in Analytic Number Theory, Markham, Chicago 1970.
  • [28] M. Knopp, Rademacher on J(τ), Poincaré series of nonpositive weights and the Eichler cohomology, Notices Amer. Math. Soc. 37 (1990), 385-393.
  • [29] O. Körner, Übertragung des Goldbach-Vinogradovschen Satzes auf reell-quadratische Zahlkörper, Math. Ann. 141 (1960), 343-366.
  • [30] O. Körner, Erweiterter Goldbach-Vinogradovscher Satz in beliebigen algebraischen Zahlkörpern, Math. Ann. 143 (1961), 344-378.
  • [31] O. Körner, Zur additiven Primzahltheorie algebraischer Zahlkörper, Math. Ann. 144 (1961), 97-109.
  • [32] R. S. Kulkarni, An arithmetic-geometric method in the study of the subgroups of the modular group, Amer. J. Math. 113 (1991), 1053-1133.
  • [33] D. H. Lehmer, The Hardy-Ramanujan series for the partition function, J. London Math. Soc. 12 (1937), 171-176.
  • [34] D. H. Lehmer, On the series for the partition function, Trans. Amer. Math. Soc. 43 (1938), 271-295.
  • [35] J. Lehner, Ramanujan identities involving the partition function for the moduli $11^a$, Amer. J. Math. 65 (1943), 492-520.
  • [36] J. Lehner, Proof of Ramanujan's partition congruence for the modulus 11³, Proc. Amer. Math. Soc. 1 (1950), 172-181.
  • [37] J. Lehner, The Fourier coefficients of automorphic forms belonging to a class of horocyclic groups, Michigan Math. J. 4 (1957), 265-279.
  • [38] J. Lehner, Partial fraction decompositions and expansions of zero, Trans. Amer. Math. Soc. 87 (1958), 130-143.
  • [39] J. Lehner, The Fourier coefficients of automorphic forms on horocyclic groups, II, Michigan Math. J. 6 (1959), 173-193.
  • [40] J. Lehner, The Fourier coefficients of automorphic forms on horocyclic groups, III, Michigan Math. 7 (1960), 65-74.
  • [41] L. J. Mordell, Lattice points in a tetrahedron and generalized Dedekind sums, J. Indian Math. Soc. 15 (1951), 41-46.
  • [42] G. Myerson, Dedekind sums and uniform distribution, J. Number Theory 28 (1988), 233-239.
  • [43] M. Newman, Remarks on some modular identities, Trans. Amer. Math. Soc. 73 (1952), 313-320.
  • [44] H. Petersson, Über die Entwicklungskoeffizienten der automorphen Formen, Acta Math. 58 (1932), 169-215.
  • [45] H. Petersson, Die linearen Relationen zwischen den ganzen Poincaréschen Reihen von reeller Dimension zur Modulgruppe, Abh. Math. Sem. Univ. Hamburg 12 (1938), 415-472.
  • [46] L. Pinzur, On a question of Rademacher concerning Dedekind sums, Proc. Amer. Math. Soc. 61 (1976), 11-15.
  • [47] C. Pommerenke, On Bloch functions, J. London Math. Soc. (2) 2 (1970), 689-695.
  • [48] J. E. Pommersheim, Lattice points in a tetrahedron and toric varieties ; Dedekind sum relations and toric varieties, submitted for publication.
  • [49] K. G. Ramanathan, Ramanujan and the congruence properties of partitions, Proc. Indian Acad. Sci. (Math. Sci.) 89 (1980), 133-157.
  • [50] S. Ramanujan, Collected Papers, Chelsea, New York 1962.
  • [51] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi 1988.
  • [52] B. Riemann, Fragmente über die Grenzfälle der elliptischen Modulfunktionen, in: Gesammelte Mathematische Werke, Dover, New York 1953, 455-465.
  • [53] K. H. Rosen, On the sign of some Dedekind sums, J. Number Theory 9 (1977), 209-212.
  • [54] K. H. Rosen, Lattice points in four-dimensional tetrahedra and a conjecture of Rademacher, J. Reine Angew. Math. 307/308 (1979), 264-275.
  • [55] L. A. Rubel and E. G. Straus, Special trigonometric series and the Riemann hypothesis, Math. Scand. 18 (1966), 35-44.
  • [56] W. Schnee, Die Funktionalgleichung der Zetafunktion und der Dirichletschen Reihen mit periodischen Koeffizienten, Math. Z. 31 (1930), 378-390.
  • [57] A. Selberg, Reflections around the Ramanujan centenary, in: Collected Papers, Vol. 1, Springer, Berlin 1989, 695-706.
  • [58] C. L. Siegel, A simple proof of η(-1/τ)=η(τ)√τ/i, Mathematika 1 (1954), 4.
  • [59] J. L. Walsh, A closed set of normal, orthogonal functions, Amer. J. Math. 55 (1923), 5-24.
  • [60] G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. 179 (1938), 97-128.
  • [61] A. Weil, Sur une formule classique, J. Math. Soc. Japan 20 (1968), 400-402.
  • [62] A. Whiteman, A sum connected with the series for the partition function, Pacific J. Math. 6 (1956), 159-176.
  • [63] H. S. Zuckerman, On the coefficients of certain modular forms belonging to subgroups of the modular group, Trans. Amer. Math. Soc. 45 (1939), 298-321.
  • [64] H. S. Zuckerman, On the expansions of certain modular forms of positive dimension, Amer. J. Math. 62 (1940), 127-152.
Typ dokumentu
Bibliografia
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