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The Doi-Naganuma lifting of quaternary theta series. (English) Zbl 0441.10025

MSC:

11F11 Holomorphic modular forms of integral weight
11E45 Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)
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References:

[1] Doi, K., Naganuma, H.: On the functional equation of certain Dirichlet series. Inventiones Math.9, 1-14 (1969) · Zbl 0182.54301 · doi:10.1007/BF01389886
[2] Eichler, M.: Quadratische Formen und orthogonale Gruppen. Berlin, Göttingen, Heidelberg: Springer 1952 · Zbl 0049.31106
[3] Eichler, M.: Zur Zahlentheorie der Quanternionen-Algebren. J. Reine Angew. Math.195, 127-151 (1955) · Zbl 0068.03303 · doi:10.1515/crll.1955.195.127
[4] Eichler, M.: On theta functions of real algebraic number fields. Acta Arith.33, 269-292 (1977) · Zbl 0348.10017
[5] Eichler, M.: Theta functions over ? and over \(\mathbb{Q}(\sqrt q \) .Modular functions of one variable. VILecture Notes in Mathematics, Vol. 627, pp. 197-225). Berlin, Heidelberg, New York: Springer 1976
[6] Hecke, E.: Mathematische Werke. Göttingen: Vandenhoeck and Ruprecht 1970 · Zbl 0205.28902
[7] Kitaoka, Y.: Quaternary even positive definite quadratic forms of prime discriminant. Nagoya Math. J.52, 147-161 (1973) · Zbl 0294.10014
[8] Kitaoka, Y.: Class numbers of quadratic forms over real quadratic fields. Nagoya Math. J.66, 89-98 (1977) · Zbl 0352.10009
[9] Naganuma, H.: On the coincidence of two Dirichlet series associated with cusp forms of Hecke’s ?Neben?-type and Hilbert modular forms over a real quadratic fields. J. Math. Soc. Japan25, 547-555 (1973) · Zbl 0259.10023 · doi:10.2969/jmsj/02540547
[10] Ponomarev, P.: Arithmetic of quaternary quadratic forms. Acta Arith.29, 1-48 ((1976). · Zbl 0321.10023
[11] Ponomarev, P.: A correspondence between quaternary quadratic forms. Nagoya Math. I62, 125-140 (1976) · Zbl 0314.10014
[12] Ponomarev, P.: Ternary quadratic forms and Shimura’s correspondence (to appear) · Zbl 0452.10030
[13] Vignéras, M.-F.: Invariants numériques des groupes de Hilbert. Math. Ann.224, 189-215 (1976) · Zbl 0325.12004 · doi:10.1007/BF01459845
[14] Waldspurger, J.-L.: Formes quadratiques à 4 variables et relèvement (to appear) · Zbl 0362.10025
[15] Zagier, D.: Modular forms associated to real quadratic fields. Inventiones Math.30, 1-46 (1975) · Zbl 0308.10014 · doi:10.1007/BF01389846
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