Abstract
In these lectures, we will prove that the modular curves X0(N) are defined over ℚ. We will also develop the q-expansions of some modular forms on these curves and construct the Hecke correspondences. We will then prove the Eichler-Shimura congruence relation, which will be used to show that the zeta function of these curves is a product of automorphic L-functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Knapp, Elliptic Curves, Mathematical Notes 40, Princeton University Press, 1992.
J.-P. Serre, A Course in Arithmetic, Graduate Texts in Mathematics, Vol 7, Springer, 1973.
Parvati Shastri, Elliptic Functions, this volume.
G. Shimura, Arithmetic Theory of automorphic functions, Princeton University Press, 1971.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Hindustan Book Agency
About this chapter
Cite this chapter
Venkataramana, T.N. (2003). On the Eichler-Shimura Congruence Relation. In: Bhandari, A.K., Nagaraj, D.S., Ramakrishnan, B., Venkataramana, T.N. (eds) Elliptic Curves, Modular Forms and Cryptography. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-15-6_18
Download citation
DOI: https://doi.org/10.1007/978-93-86279-15-6_18
Publisher Name: Hindustan Book Agency, Gurgaon
Print ISBN: 978-81-85931-42-5
Online ISBN: 978-93-86279-15-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)