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Modular forms and the Shimura-Taniyama Conjecture

In: Six Short Chapters on Automorphic Forms and L-functions

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  • Ze-Li Dou

    (Texas Christian University, Department of Mathematics)

  • Qiao Zhang

    (Texas Christian University, Department of Mathematics)

Abstract

The concept of modular form are based on very natural considerations. In this chapter we recount some rudiments of the theory of modular forms without assuming any previous knowledge of the subject on the reader’s part. The number theoretic interest of the subject becomes apparent when we describe the Hecke operators on the spaces of modular forms and the L-functions attached to eigenforms. The connection between elliptic curves and modular forms of weight 2 is briefly described towards the end in order to state the celebrated Shimura-Taniyama Conjecture, which is now a theorem of A. Wiles, et al. See [Wi95] and related articles.

Suggested Citation

  • Ze-Li Dou & Qiao Zhang, 2012. "Modular forms and the Shimura-Taniyama Conjecture," Springer Books, in: Six Short Chapters on Automorphic Forms and L-functions, chapter 0, pages 1-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-28708-4_1
    DOI: 10.1007/978-3-642-28708-4_1
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