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註釋Researchers found the concept of Hecke operators so cool that they immediately started developing a version for modular forms. In no time it became apparent that the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Here young researchers and graduate students working in algebra and number theory are introduced to this beautiful and mysterious realm of number theory. Begins with the basics and ends with the latest results, explaining the current status of applications to spaces of holomorphic modular forms of integer and half-integer weigh congruence-subgroups of integral symplectic groups. Essentially considers Hecke operators as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. Translated from the 1992 Moduliarnye formy i operatory Gekke. No index. Annotation copyright by Book News, Inc., Portland, OR