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Ternary quadratic forms and Brandt matrices

Published online by Cambridge University Press:  22 January 2016

Rainer Schulze-Pillot
Rainer Schulze-Pillot*
Affiliation:
Freie Universität, Berlin Institut für Mathematik II, Arnimallee 3, 1000 Berlin (West) 33
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In a recent paper [9] the author showed (among other results) estimates on the asymptotic behaviour of the representation numbers of positive definite integral ternary quadratic forms, in particular, that for n in a fixed square class tZ2 and lattices L, K in the same spinor genus one has . The main tool utilized for the proof was the theory of modular forms of weight 3/2, especially Shimura’s lifting from the space of cusp forms of weight 3/2 to the space of modular forms of weight 2.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 102 , June 1986, pp. 117 - 126
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[ 1 ] Eichler, M., Quadratische Formen und orthogonale Gruppen, Berlin-GöttingenHeidelberg: Springer 1952.Google Scholar
[ 2 ] Eichler, M., Quaternäre quadratische Formen und die Riemannsche Vermutung fur Kongruenzzetafunktionen, Arch. Math., 5 (1954), 355–366.Google Scholar
[ 3 ] Eichler, M., The basis problem for modular forms and the traces of the Hecke operators, Modular functions of one variable I, Lecture notes in Mathematics, Vol. 320, pp. 75–151, Berlin-Heidelberg-New York: Springer 1973.Google Scholar
[ 4 ] Eichler, M., On theta functions in real algebraic number fields, Acta Arith., 33 (1977), 269–292.Google Scholar
[ 5 ] Gundlach, K.-B., Über die Darstellung der ganzen Spitzenformen zu den Idealstufen der Hilbertschen Modulgruppe und die Abschätzung ihrer Fourierkoeffizienten, Acta math., 92 (1954), 309–345.Google Scholar
[ 6 ] Ponomarev, P., Ternary quadratic forms and Shimura’s correspondence, Nagoya Math. J., 81 (1981), 123–151.Google Scholar
[ 7 ] Rallis, S., The Eichler commutation relation and the continuous spectrum of the Weil representation, Non commutative harmonic analysis, Proc. Marseille-Luminy 1978, Lecture Notes in Mathematics, Vol. 728, pp. 211–244. Berlin-Heidelberg-New York: Springer 1979.Google Scholar
[ 8 ] Schulze-Pillot, R., Darstellung durch definite temare quadratische Formen, J. of Number Theory, 14 (1982), 237–250.Google Scholar
[ 9 ] Schulze-Pillot, R., Thetareihen positiv definiter quadratischer Formen, Invent. Math., 75 (1984), (1984), 283–299.Google Scholar
[10] Schulze-Pillot, R., Darstellungsmafie von Spinorgeschlechtern ternärer quadratischer Formen, J. reine und angew. Math., 252 (1984), 114–132.Google Scholar
[11] Shimura, G., On modular forms of half integral weight, Ann. of Math., 97 (1973), 440–481.Google Scholar