Hans Rademacher (1892-1969)

Bruce C. Berndt

Acta Arithmetica (1992)

  • Volume: 61, Issue: 3, page 209-225
  • ISSN: 0065-1036

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Bruce C. Berndt. "Hans Rademacher (1892-1969)." Acta Arithmetica 61.3 (1992): 209-225. <http://eudml.org/doc/206463>.

@article{BruceC1992,
author = {Bruce C. Berndt},
journal = {Acta Arithmetica},
keywords = {biography},
language = {eng},
number = {3},
pages = {209-225},
title = {Hans Rademacher (1892-1969)},
url = {http://eudml.org/doc/206463},
volume = {61},
year = {1992},
}

TY - JOUR
AU - Bruce C. Berndt
TI - Hans Rademacher (1892-1969)
JO - Acta Arithmetica
PY - 1992
VL - 61
IS - 3
SP - 209
EP - 225
LA - eng
KW - biography
UR - http://eudml.org/doc/206463
ER -

References

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  1. [1] L. V. Ahlfors, An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938), 359-364. Zbl64.0315.04
  2. [2] G. E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, Mass., 1976. Zbl0371.10001
  3. [3] A. O. L. Atkin, Proof of a conjecture of Ramanujan, Glasgow Math. J. 8 (1967), 67-78. Zbl0163.04302
  4. [4] B. C. Berndt, Generalized Dedekind eta-functions and generalized Dedekind sums, Trans. Amer. Math. Soc. 178 (1973), 495-508. Zbl0262.10015
  5. [5] B. C. Berndt, Generalized Eisenstein series and modified Dedekind sums, J. Reine Angew. Math. 272 (1975), 182-193. Zbl0294.10018
  6. [6] B. C. Berndt, Reciprocity theorems for Dedekind sums and generalizations, Adv. in Math. 23 (1977), 285-316. Zbl0342.10014
  7. [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. Zbl0384.10011
  8. [8] R. W. Bruggeman, Dedekind sums and Fourier coefficients of modular forms, J. Number Theory 36 (1990), 289-321. Zbl0723.11018
  9. [9] Y. Chuman, Generators and relations of Γ₀(N), J. Math. Kyoto Univ. 13 (1973), 381-390. 
  10. [10] H. Davenport, Multiplicative Number Theory, 2nd ed., Springer, New York 1980. Zbl0453.10002
  11. [11] R. Dedekind, Erläuterungen zu zwei Fragmenten von Riemann, in: Gesammelte Mathematische Werke, Friedr. Vieweg & Sohn, Braunschweig 1930, 159-172. 
  12. [12] H. Frasch, Die Erzeugenden der Hauptkongruenzgruppen für Primzahlstufen, Math. Ann. 108 (1933), 229-252. Zbl59.0146.04
  13. [13] L. A. Goldberg, Transformations of Theta-functions and Analogues of Dedekind Sums, Ph.D. Dissertation, University of Illinois at Urbana-Champaign, 1981. 
  14. [14] E. Grosswald, On the structure of some subgroups of the modular group, Amer. J. Math. 72 (1950), 809-834. Zbl0040.30003
  15. [15] E. Grosswald, On the parabolic generators of the principal congruence subgroups of the modular group, Amer. J. Math. 74 (1952), 435-443. Zbl0046.31202
  16. [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. Zbl0476.01004
  17. [17] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, New York 1974. Zbl0298.10026
  18. [18] G. H. Hardy, Collected Papers, Vol. 1, Clarendon Press, Oxford 1966. 
  19. [19] G. H. Hardy and J. E. Littlewood, Some problems of Diophantine approximation. I. The fractional part of , Acta Math. 37 (1914), 155-191. Zbl45.0305.03
  20. [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. Zbl48.0143.04
  21. [21] G. H. Hardy and S. Ramanujan, Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. (2) 17 (1918), 75-115. Zbl46.0198.04
  22. [22] E. Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen. Zweite Mitteilung, Math. Z. 6 (1920), 11-51. 
  23. [23] E. Hecke, Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktenwicklung. I, Math. Ann. 114 (1937), 1-28. Zbl0015.40202
  24. [24] E. Hecke, Mathematische Werke, Vandenhoeck & Ruprecht, Göttingen 1970. 
  25. [25] D. R. Hickerson, Continued fractions and density results for Dedekind sums, J. Reine Angew. Math. 290 (1977), 113-116. Zbl0341.10012
  26. [26] F. John, Identitäten zwischen dem Integral einer willkürlichen Funktion und unendlichen Reihen, Math. Ann. 110 (1935), 718-721. Zbl61.0247.01
  27. [27] M. Knopp, Modular Functions in Analytic Number Theory, Markham, Chicago 1970. 
  28. [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. [29] O. Körner, Übertragung des Goldbach-Vinogradovschen Satzes auf reell-quadratische Zahlkörper, Math. Ann. 141 (1960), 343-366. Zbl0099.03602
  30. [30] O. Körner, Erweiterter Goldbach-Vinogradovscher Satz in beliebigen algebraischen Zahlkörpern, Math. Ann. 143 (1961), 344-378. Zbl0103.02901
  31. [31] O. Körner, Zur additiven Primzahltheorie algebraischer Zahlkörper, Math. Ann. 144 (1961), 97-109. 
  32. [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. Zbl0758.11024
  33. [33] D. H. Lehmer, The Hardy-Ramanujan series for the partition function, J. London Math. Soc. 12 (1937), 171-176. Zbl0017.05601
  34. [34] D. H. Lehmer, On the series for the partition function, Trans. Amer. Math. Soc. 43 (1938), 271-295. Zbl0018.10703
  35. [35] J. Lehner, Ramanujan identities involving the partition function for the moduli , Amer. J. Math. 65 (1943), 492-520. Zbl0060.10007
  36. [36] J. Lehner, Proof of Ramanujan's partition congruence for the modulus 11³, Proc. Amer. Math. Soc. 1 (1950), 172-181. Zbl0037.31303
  37. [37] J. Lehner, The Fourier coefficients of automorphic forms belonging to a class of horocyclic groups, Michigan Math. J. 4 (1957), 265-279. Zbl0081.07602
  38. [38] J. Lehner, Partial fraction decompositions and expansions of zero, Trans. Amer. Math. Soc. 87 (1958), 130-143. Zbl0085.29201
  39. [39] J. Lehner, The Fourier coefficients of automorphic forms on horocyclic groups, II, Michigan Math. J. 6 (1959), 173-193. Zbl0085.30003
  40. [40] J. Lehner, The Fourier coefficients of automorphic forms on horocyclic groups, III, Michigan Math. 7 (1960), 65-74. Zbl0093.08202
  41. [41] L. J. Mordell, Lattice points in a tetrahedron and generalized Dedekind sums, J. Indian Math. Soc. 15 (1951), 41-46. Zbl0043.05101
  42. [42] G. Myerson, Dedekind sums and uniform distribution, J. Number Theory 28 (1988), 233-239. Zbl0635.10033
  43. [43] M. Newman, Remarks on some modular identities, Trans. Amer. Math. Soc. 73 (1952), 313-320. Zbl0047.04303
  44. [44] H. Petersson, Über die Entwicklungskoeffizienten der automorphen Formen, Acta Math. 58 (1932), 169-215. Zbl58.1110.01
  45. [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. Zbl0019.34403
  46. [46] L. Pinzur, On a question of Rademacher concerning Dedekind sums, Proc. Amer. Math. Soc. 61 (1976), 11-15. Zbl0314.10002
  47. [47] C. Pommerenke, On Bloch functions, J. London Math. Soc. (2) 2 (1970), 689-695. 
  48. [48] J. E. Pommersheim, Lattice points in a tetrahedron and toric varieties ; Dedekind sum relations and toric varieties, submitted for publication. Zbl0789.14043
  49. [49] K. G. Ramanathan, Ramanujan and the congruence properties of partitions, Proc. Indian Acad. Sci. (Math. Sci.) 89 (1980), 133-157. Zbl0447.10016
  50. [50] S. Ramanujan, Collected Papers, Chelsea, New York 1962. 
  51. [51] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi 1988. Zbl0639.01023
  52. [52] B. Riemann, Fragmente über die Grenzfälle der elliptischen Modulfunktionen, in: Gesammelte Mathematische Werke, Dover, New York 1953, 455-465. 
  53. [53] K. H. Rosen, On the sign of some Dedekind sums, J. Number Theory 9 (1977), 209-212. Zbl0349.10005
  54. [54] K. H. Rosen, Lattice points in four-dimensional tetrahedra and a conjecture of Rademacher, J. Reine Angew. Math. 307/308 (1979), 264-275. Zbl0402.10047
  55. [55] L. A. Rubel and E. G. Straus, Special trigonometric series and the Riemann hypothesis, Math. Scand. 18 (1966), 35-44. Zbl0147.02901
  56. [56] W. Schnee, Die Funktionalgleichung der Zetafunktion und der Dirichletschen Reihen mit periodischen Koeffizienten, Math. Z. 31 (1930), 378-390. 
  57. [57] A. Selberg, Reflections around the Ramanujan centenary, in: Collected Papers, Vol. 1, Springer, Berlin 1989, 695-706. 
  58. [58] C. L. Siegel, A simple proof of η(-1/τ)=η(τ)√τ/i, Mathematika 1 (1954), 4. 
  59. [59] J. L. Walsh, A closed set of normal, orthogonal functions, Amer. J. Math. 55 (1923), 5-24. Zbl49.0293.03
  60. [60] G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. 179 (1938), 97-128. Zbl0019.15302
  61. [61] A. Weil, Sur une formule classique, J. Math. Soc. Japan 20 (1968), 400-402. 
  62. [62] A. Whiteman, A sum connected with the series for the partition function, Pacific J. Math. 6 (1956), 159-176. Zbl0071.04004
  63. [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. Zbl65.0352.01
  64. [64] H. S. Zuckerman, On the expansions of certain modular forms of positive dimension, Amer. J. Math. 62 (1940), 127-152. Zbl66.0373.01

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