Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literature
COHEN H., Formes modulaires à une et deux variables, Thèse 1976, Université de Bordeaux I
EICHLER M., Quadratische Formen und orthogonale Gruppen, 2. Aufl. Springer Verlag, Berlin-Heidelberg-New York 1974.
EICHLER M., Zur Zahlentheorie der Quaternionen-Algebren, Journal reine und angew. Math. 195 (1956), 127–151.
EICHLER M., Quadratische Formen und Modulfunktionen, Acta Arithmetica 4 (1958), 217–239.
EICHLER M., The basis problem for modular forms and the traces of Hecke operators, in Modular Forms of One Variable I, Lecture Notes in Mathematics nr. 320, Springer Verlag, Berlin-Heidelberg-New York 1973.
EICHLER M., On theta functions in real algebraic number fields, to appear in Acta Arithmetica.
HIJIKATA H. and SAITO H., On the representability of modular forms by theta series, p. 13–21 in Number Theory, Algebraic Geometry, and Commutative Algebra, a volume published in honor of Y. Akizuki, Kinokuniya, Tokyo 1973.
NAGANUMA H., On the coincidence of two Dirichlet series associated with cusp forms of Hecke's “nebentype” and Hilbert modular forms over real quadratic fields, Journ. Math. Soc. Japan (4) 25 (1973), 547–555.
PETERS M., Ternäre und quaternäre quadratische Formen und Quaternionenalgebren, Acta Arithmetica 15 (1969), 319–365.
SAITO H., Automorphic forms and algebraic extensions of number fields, Lecture Note in Mathematics nr. 8, Kyoto Univ. 1975.
SHIMIZU H., On traces of Hecke operators, Journ. Fac. Sci. Univ. Tokyo 10 (1963), 1–19.
ZAGIER D., Modular forms associated to real quadratic fields, Inventiones Math. 30 (1975), 1–46.
O'MEARA O.T., Introduction to Quadratic Forms, Springer Verlag, Berlin-Heidelberg-New York, 1963.
Editor information
Rights and permissions
Copyright information
© 1977 Springer-Verlag
About this paper
Cite this paper
Eichler, M. (1977). Theta functions over Q and over Q(√q). In: Serre, JP., Zagier, D.B. (eds) Modular Functions of One Variable VI. Lecture Notes in Mathematics, vol 627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065302
Download citation
DOI: https://doi.org/10.1007/BFb0065302
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08530-0
Online ISBN: 978-3-540-35984-5
eBook Packages: Springer Book Archive