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Literaturverzeichnis

  1. N. G. Bakhoom. Asymptotic expansions of the function \({f_k}\left( x \right) = {\text{ }}\int_0^\infty {{e^{ - {u^k} + xu}}du} \) du . Proc. London Math. Soc. (2),35: 83–100, 1933.

    Google Scholar 

  2. H. Bateman and A. Erdelyi. Higher Transcendental Functions I. Mc Graw-Hill Book Company, Inc., New York, Toronto, London, 1953.

    MATH  Google Scholar 

  3. H. Bateman and A. Erdelyi. Higher Transcendental Functions II. Mc Graw-Hill Book Company, Inc., New York, Toronto, London, 1953.

    MATH  Google Scholar 

  4. V. Bentkus and F. Götze. On the lattice point problem for ellipsoid. Acta Arith.,2: 101–125, 1997.

    Google Scholar 

  5. T. Bonnesen and W. Fenchel. Theorie der konvexen Körper. Springer-Verlag, Berlin, 1934.

    MATH  Google Scholar 

  6. J. W. S. Cassels. An Introduction to Diophantine Approximation. Cambridge University Press, Cambridge, 1965.

    Google Scholar 

  7. J. W. S. Cassels. An Introduction to the Geometry of Numbers. Springer-Verlag, Berlin-Heidelberg-New York, 1971.

    MATH  Google Scholar 

  8. F. Chamizo. Lattice points in bodies of revolution. Acta Arith.,85: 265–277, 1998.

    MATH  MathSciNet  Google Scholar 

  9. F. Chamizo and H. Iwaniec. On the sphere problem. Rev. Mat. Iberoamericana, 11: 417–429, 1995.

    MATH  MathSciNet  Google Scholar 

  10. R. Cooper. The behaviour of certain series associated with limiting cases of elliptic theta-functions. Proc. London Math. Soc. (2),27: 410–426, 1928.

    Article  MATH  Google Scholar 

  11. E. T. Copson. Asymptotic Expansions. At the University Press,Cambridge, 1965.

    Google Scholar 

  12. Y. Colin de Verdiere. Normbres de points dans une famille homothetique de domaines de Rte. Ann. Sci. Ecole Norm. Sup.,10: 559–576, 1977.

    MATH  MathSciNet  Google Scholar 

  13. G. Doetsch. Handbuch der Laplace-Transformation I. Birkhäuser, Basel, 1950.

    MATH  Google Scholar 

  14. G. Doetsch. Handbuch der Laplace-Transformation II. Birkhäuser, Basel, 1953.

    Google Scholar 

  15. G. Doetsch. Handbuch der Laplace-Transformation III. Birkhäuser, Basel, 1956.

    MATH  Google Scholar 

  16. F. Fricker. Einführung in die Gitterpunktlehre. Birkhäuser, Basel-BostonStuttgart, 1982.

    MATH  Google Scholar 

  17. S. W. Graham and G. Kolesnik. Van der Corput’s Method of Exponential Sums. London Math. Soc., Lecture Note Series 126, 1991.

    Google Scholar 

  18. P. M. Gruber and C. G. Lekkerkerker. Geometry of Numbers. North-Holland, Amsterdam, 1987.

    MATH  Google Scholar 

  19. P. M. Gruber and J. M. Wills. Handbook of Convex Geometry. North-Holland, Amsterdam-New York-Tokyo, 1993.

    Google Scholar 

  20. K. Haberland. Ueber die Anzahl von Gitterpunkten in konvexen Gebieten. Preprint,1993.

    Google Scholar 

  21. H. Hadwiger. Altes und Neues über konvexe Körper. Birkhäuser, Basel, 1955.

    MATH  Google Scholar 

  22. H. Hadwiger and J. M. Wills. Gitterpunktanzahl konvexer Rotationskörper. Math. Ann., 208: 221–232, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  23. G. H. Hardy and J. E. Littlewood. Some problems of Diophantine approximation ii. the trigonometrical series associated with the elliptic 29-functions. Acta Math.,37: 193–238, 1914.

    Article  MathSciNet  Google Scholar 

  24. H. Hasse. Vorlesungen über Zahlentheorie. Springer-Verlag, Berlin-GöttingenHeidelberg, 1950.

    MATH  Google Scholar 

  25. D. R. Heath-Brown. Weyl’s inequality, Hua’s inequality and Waring’s problem. J. London Math. Soc., 38: 216–230, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  26. D. R. Heath-Brown. Lattice points in the sphere. Proc. Number Theory Conf. Zakopane, Poland, 1997.

    Google Scholar 

  27. D. R. Heath-Brown and S. J. Patterson. The distribution of Kummer sums at prime arguments. J. Reine Angew. Math., 310: 111–136, 1979.

    MATH  MathSciNet  Google Scholar 

  28. E. Hlawka. Ueber die Zetafunktion konvexer Körper. Monatsh. Math., 54: 100–107, 1950.

    Article  MATH  MathSciNet  Google Scholar 

  29. E. Hlawka. Ueber Integrale auf konvexen Körpern I. Monatsh. Math.,54: 1–36, 1950.

    Article  MathSciNet  Google Scholar 

  30. E. Hlawka. Ueber Integrale auf konvexen Körpern II. Monatsh. Math., 54: 81–99, 1950.

    Article  MathSciNet  Google Scholar 

  31. M. N. Huxley. Area,Lattice Points and Exponential Sums. Clarendon Press, Oxford, 1996.

    Google Scholar 

  32. S. Iseki. The transformation formula for the Dedekind modular function and related functional equations. Duke Math. J., 24: 653–662, 1957.

    Article  MATH  MathSciNet  Google Scholar 

  33. S. Iseki. A generalization of a functional equation related to the theory of partitions. Duke Math. J., 27: 96–110, 1960.

    Article  MathSciNet  Google Scholar 

  34. J. Karamata and M. Tomic. Sur une inegalite de Kusmin-Landau relative aux sommes trigonometriques et son application a la somme de Gauss. Publ. Inst. Math. Acad. Serbe Sci.,3: 207–218, 1950.

    MathSciNet  Google Scholar 

  35. A. Khintchine. Kettenbrüche. Teubner, Leipzig, 1956.

    MATH  Google Scholar 

  36. M. I. Knopp. Modular Functions in Analytic Number Theory. Markham Publishing Company, Chicago, 1970.

    MATH  Google Scholar 

  37. J. F. Koksma. Diophantische Approximationen. Springer, Berlin, 1936.

    Google Scholar 

  38. N. M. Korobov. Exponential Sums and their Applications. Kluwer Academic Publishers, Dordrecht/Boston/London, 1992.

    MATH  Google Scholar 

  39. E. Krätzel. Ein Reziprozitätsgesetz für eine Reihe über Bessel-Funktionen. Archiv Math.,16: 449–451, 1965.

    Article  MATH  Google Scholar 

  40. E. Krätzel. Höhere Thetafunktionen I. Math. Nachr., 30: 17–32, 1965.

    Article  Google Scholar 

  41. E. Krätzel. Höhere Thetafunktionen II. Math. Nachr., 30: 33–46, 1965.

    Article  MathSciNet  Google Scholar 

  42. E. Krätzel. Kubische und biquadratische Gaußsche Summen J. Reine Angew. Math., 228: 159–165, 1967.

    Article  MATH  MathSciNet  Google Scholar 

  43. E. Krätzel. Zur Frage der Produktentwicklung höherer Thetafunktionen. Math. Nachr., 71: 291–302, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  44. E. Krätzel. Dedekindsche Funktionen und Summen I. Period. Math. Hungar., 12: 113–123, 1981.

    Article  MATH  MathSciNet  Google Scholar 

  45. E. Krätzel. Dedekindsche Funktionen und Summen II. Period. Math. Hungar., 12: 163–179, 1981.

    Article  MathSciNet  Google Scholar 

  46. E. Krätzel. Zahlentheorie. Dt. Verlag d. Wiss., Berlin, 1981.

    Google Scholar 

  47. E. Krätzel. Lattice Points. Dt. Verlag d. Wiss., Berlin und Kluwer Academic Publishers Dordrecht/Boston/London, 1988.

    Google Scholar 

  48. E. Krätzel. Double exponential sums Analysis,16: 109–123, 1996.

    MATH  MathSciNet  Google Scholar 

  49. E. Krätzel. Lattice points in large convex bodies: Analytic foundations. Proc. of the Conference on Analytic and Elementary Number Theory, Wien,pages 149–164, 1996.

    Google Scholar 

  50. E. Krätzel. Lattice points in three-dimensional large convex bodies. Math. Nachr., 2000.

    Google Scholar 

  51. E. Krätzel and W. G. Nowak. Lattice points in large convex bodies. Monatsh. Math., 112: 61–72, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  52. E. Krätzel and W. G. Nowak. Lattice points in large convex bodies II. Acta Arith., 62: 285–295, 1992.

    MATH  MathSciNet  Google Scholar 

  53. W. Maier. Transformation der kubischen Thetafunktion. Math. Ann., 111: 183–196, 1935.

    Article  MathSciNet  Google Scholar 

  54. H. Mellin. Eine Formel für den Logarithmus transcendenter Funktionen von endlichem Geschlecht. Acta Math., 25: 165–183, 1901.

    Article  MATH  MathSciNet  Google Scholar 

  55. H. Menzer. Transformation spezieller Dirichletscher Reihen I. Math. Nachr., 73: 297–303, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  56. H. Menzer. Transformation spezieller Dirichletscher Reihen II. Math. Nachr., 73: 305–313, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  57. L. J. Mordell. On a simple summation of the series Th. Messenger of Math., 48: 54–56, 1918.

    Google Scholar 

  58. L. J. Mordell. On the Kusmin-Landau inequality for exponential sums. Acta Arith.,4: 3–9, 1958.

    MATH  MathSciNet  Google Scholar 

  59. W. Müller. Lattice points in large convex bodies. Monatsh. Math., 2000.

    Google Scholar 

  60. W. Müller and W. G. Nowak. On lattice points in planar domains. Math. J. Okayama University,27: 173–184, 1985.

    MATH  Google Scholar 

  61. W. G. Nowak. Zur Gitterpunktlehre der euklidischen Ebene. Indagationes math.,46: 209–223, 1984.

    MATH  Google Scholar 

  62. W. G. Nowak. On the lattice rest of a convex body in Rs. Arch. Math., 45: 284–288, 1985.

    Article  MATH  Google Scholar 

  63. W. G. Nowak. Zur Gitterpunktlehre der euklidischen Ebene II. Mitteilungen d. Wiener Akademie d. Wiss.,pages 31–37, 1985.

    Google Scholar 

  64. W. G. Nowak. On the lattice rest of a convex body in RS II. Arch. Math., 47: 232–237, 1986.

    Article  MATH  Google Scholar 

  65. W. G. Nowak. Topics in lattice point theory I (japanisch). Sugaka Seminar, 291: 79–89, 1986.

    Google Scholar 

  66. W. G. Nowak. On the lattice rest of a convex body in RS III. Czechosl. Math. J.,41: 359–367, 1991.

    Google Scholar 

  67. H. Pieper. Variationen über ein zahlentheoretisches Thema von C. F. Gauss. Dt. Verlag d. Wiss., Berlin, 1978.

    Google Scholar 

  68. L. P. Postnikova. Trigonometrische Summen und die Theorie der Kongruenzen nach einem Primzahlmodul (russ.). Pädagogisches Institut Moskau, 1973.

    Google Scholar 

  69. H. Rademacher. Topics in Analytic Number Theory. Springer Berlin, Heidelberg, New York, 1973.

    MATH  Google Scholar 

  70. B. Randol. On the Fourier transform of the indicator function of a planar set. Trans. Amer. Math. Soc., 139: 271–278, 1969.

    MATH  MathSciNet  Google Scholar 

  71. P. G. Schmidt. Zur Anzahl unitärer Faktoren abelscher Gruppen. Acta Arith.,64: 237–248, 1993.

    MATH  MathSciNet  Google Scholar 

  72. W. M. Schmidt. Diophantine Approximations. Springer-Verlag, BerlinHeidelberg-New York, 1980.

    Google Scholar 

  73. M. Tarnopolska-Weiss. On the number of lattice points in planar domains. Proc. Am. Math. Soc.,69: 308–311, 1978.

    Article  MathSciNet  Google Scholar 

  74. E. C. Titchmarsh and D. R. Heath-Brown. The Theory of the Riemann Zeta-Function. At the Clarendon Press, Oxford, 1986.

    Google Scholar 

  75. J. D. Vaaler. Some extremal problems in Fourier analysis. Bull. Am. Math. Soc.,12: 183–216, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  76. A. Walfisz. Weylsche Exponentialsummen in der neueren Zahlentheorie. Deutscher Verlag der Wissenschaften, Berlin, 1963.

    MATH  Google Scholar 

  77. E. T. Whittaker and G. N. Watson. A Course of Modern Analysis. At the University Press, Cambridge, 1962.

    MATH  Google Scholar 

  78. J. M. Wills. Zur Gitterpunktanzahl konvexer Mengen. Elem. Math., 28: 57–63, 1973.

    MATH  MathSciNet  Google Scholar 

  79. J. M. Wright. Asymptotic partition formulae III. Acta Math.,63: 143–191, 1934.

    Article  MathSciNet  Google Scholar 

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Krätzel, E. (2000). Literaturverzeichnis. In: Analytische Funktionen in der Zahlentheorie. Teubner-Texte zur Mathematik, vol 139. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-80021-3_6

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