Algebraic Number Theory
Hecke operators are a family of linear operators that act on modular forms and are crucial for the study of modular forms and their connections to number theory. They allow for the construction of new modular forms from existing ones and play a significant role in the theory of elliptic curves, particularly in understanding their arithmetic properties. The Hecke operators facilitate the study of congruences among modular forms and help relate them to L-functions, which are key in various areas of mathematics, including algebraic geometry and number theory.
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