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Thetareihen positiv definiter quadratischer Formen

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Literatur

  1. Andrianov, A.N.: Analytic arithmetic of quadratic forms with an odd number of variables, as connected with the theory of modular forms, Doklady Ak. Nauk SSSR Tom145, 241–244 (1960); englische Übersetzung in Soviet Mathematics-Doklady3, 949–952 (1962)

    Google Scholar 

  2. Andrianov, A.N.: Action of Hecke operatorT(p) on theta series. Math. Ann.247, 245–254 (1980)

    Google Scholar 

  3. Arenstorf, R.F., Johnson, D.: Uniform distribution of integral points on 3-dimensional spheres via modular forms. J. of Number Theory11, 218–238 (1979)

    Google Scholar 

  4. Cipra, B.: On the Niwa-Shintani-Theta-kernel lifting of modular forms. Preprint

  5. Earnest, A.G.: Representation of spinor exceptional integers by ternary quadratic forms. Preprint

  6. Eichler, M.: Quadratische Formen und orthogonale Gruppen. Berlin-Göttingen-Heidelberg: Springer 1952

    Google Scholar 

  7. Eichler, M.: Die Ähnlichkeitsklassen indefiniter Gitter. Math. Z.55, 216–252 (1952)

    Google Scholar 

  8. Eichler, M.: Quaternäre quadratische Formen und die Riemannsche Vermutung für die Kongruenzzetafunktionen. Arch. math.5, 355–366 (1954)

    Google Scholar 

  9. Flicker, Y.: Automorphic forms on covering groups ofGL(2). Invent. Math.57, 119–182 (1980)

    Google Scholar 

  10. Gelbart, S., Piatetski-Shapiro, J.: On Shimura's correspondence for modular forms of half integral weight, Proceedings of the Colloquium on Automorphic Forms, Representation Theory and Arithmetic, Bombay, 1979

  11. Goldfeld, D., Hoffstein, J., Patterson, S.J.: On automorphic functions of half-integral weight with applications to elliptic curves. In: Number Theory related to Fermat's last theorem, Progress in Mathematics Vol. 26. Boston, Basel, Stuttgart: Birkhäuser 1982

    Google Scholar 

  12. Hecke, E.: Mathematische Werke. Vandenhoeck und Ruprecht, 2. Aufl. Göttingen 1970

  13. Hsia, J.S.: Representations by spinor genera. Pac. J. of Math.63, 147–152 (1976)

    Google Scholar 

  14. Jones, B.W., Watson, G.L.: On indefinite ternary quadratic forms. Canad. J. Math.8, 592–608 (1956)

    Google Scholar 

  15. Kitaoka, Y.: Modular forms of degreen and representation by quadratic forms II. Nagoya Math. J.87, 127–146 (1982)

    Google Scholar 

  16. Kloostermann, H.D.: Asymptotische Formeln für die Fourierkoeffizienten ganzer Modulformen. Abh. Math. Sem. Hamburg5, 337–352 (1927)

    Google Scholar 

  17. Kneser, M.: Darstellungsmaße indefiniter quadratischer Formen. Math. Z.77, 188–194 (1961)

    Google Scholar 

  18. Kneser, M.: Witts Satz für quadratische Formen über lokalen Ringen. Nachr. Akad. Wiss. Göttingen math.-Phys. K1 II 1972, 195–203

    Google Scholar 

  19. Kneser, M.: Quadratische Formen. Vorlesungsausarbeitung, Göttingen 1974

  20. Kojima, H.: Cusp forms of weight 3/2. Nagoya Math. J.79, 111–122 (1980)

    Google Scholar 

  21. Malyshev, A.V.: Yu. V. Linnik's ergodic method in number theory. Acta arithmetica27, 555–598 (1975)

    Google Scholar 

  22. Niwa, S.: Modular forms of half integral weight and the integral of certain theta-functions. Nagoya Math. J.56, 147–161 (1974)

    Google Scholar 

  23. Peters, M.: Darstellungen durch definite ternäre quadratische Formen. Acta Arith.34, 57–80 (1977)

    Google Scholar 

  24. Pfetzer, W.: Die Wirkung der Modulsubstitutionen auf mehrfache Thetareihen zu quadratischen Formen ungerader Variablenzahl. Arch. Math.4, 448–454 (1953)

    Google Scholar 

  25. Ponomarev, P.: Ternary quadratic forms and Shimura's correspondence. Nagoya Math. J.81, 123–151 (1981)

    Google Scholar 

  26. Rallis, S.: The Eichler commutation relation and the continuous spectrum of the Weil representation, Non-commutative harmonic analysis, Proceedings Marseille-Luminy. 1978. Lecture Notes in Mathematics, Vol. 728, pp. 211–244, Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  27. Schoeneberg, B.: Das Verhalten von mehrfachen Thetareihen bei Modulsubstitutionen. Math. Ann.116, 511–523 (1939)

    Google Scholar 

  28. Schulze-Pillot, R.: Darstellung durch definite ternäre quadratische Formen. J. of Number Theory14, 237–250 (1982)

    Google Scholar 

  29. Schulze-Pillot, R.: Darstellungsmaße von Spinorgeschlechtern ternärer quadratischer Formen. Erscheint demnächst

  30. Shemanske, T.: Primitive newforms of weight 3/2. Acta Arith.43 (erscheint demnächst)

  31. Shimura, G.: On modular forms of half integral weight. Ann. of Math.97, 440–481 (1973)

    Google Scholar 

  32. Shimura, G.: The critical values of certain zeta functions associated with modular forms of half integral weight. J. of the Math. Soc. of Japan33, 649–672 (1981)

    Google Scholar 

  33. Shintani, T.: On construction of holomorphic cusp forms of half integral weight. Nagoya Math. J.58, 83–126 (1975)

    Google Scholar 

  34. Siegel, C.L.: Über die analytische Theorie der quadratischen Formen, Gesammelte Abhandlungen Bd. 1, pp. 326–405. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  35. Siegel, C.L.: Indefinite quadratische Formen und Funktionentheorie I, Gesammelte Abhandlungen Bd. 3, pp. 105–142. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  36. Sturm, J.: Theta series of weight 3/2. J. of Number Theory14, 353–361 (1982)

    Google Scholar 

  37. Ting Yi Pei: Eisenstein series of weight 3/2. I. Transactions of the AMS274, 573–606 (1982)

    Google Scholar 

  38. Vigneras, M.F.: Facteurs gamma et équations fonctionnelles, Modular functions of one variable VI. Lecture Notes in Mathematics, Vol. 627, pp. 79–104. Berlin-Heidelberg-New York: Springer 1977

    Google Scholar 

  39. Waldspurger, J.-L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures et Appl.60, 375–484 (1981)

    Google Scholar 

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Schulze-Pillot, R. Thetareihen positiv definiter quadratischer Formen. Invent Math 75, 283–299 (1984). https://doi.org/10.1007/BF01388566

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