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Chapter eight of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It discusses the information on the doubling zeta integral as well as the functions of the Siegel Eisenstein series against the cusp modular forms. It cites the global doubling integrals' formulations. Information about the Waldspurger's theory is also discussed.

Chapter nine of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It discusses the formulations along with the indefinite quaternion algebra in determining the arithmetic theta lift. It highlights the computational steps for the theta lift through Rallis inner product formula. The Stein table depicting the Newforms F is also presented.

Chapter seven of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It discusses the valued generating function along with its modularity in obtaining the 0-cycles with their coefficients. It denotes the applicability of the Gross' theory in Siegel modular form. The theorems and the green functions are also discussed.

An appendix is presented of formulations and theorems in determining the special cycles within the Drinfield space.

Chapter six of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It discusses the generating function of the arithmetic Chow groups and Siegel space in obtaining the 0-cycles. Furthermore, the singular and the constant term formulations for the mentioned cycles are also presented.

Chapter five of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It explores the main derivation of the two Eisntein series which are conjugating with the indefinite quarternion algebra. It cites the formulations for nonsingular Fourier coefficients. Information about the Siegel-Weil formula is also discussed.

Chapter four of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It delineates the surface and structure of the arithmetic chow groups with real coefficients. It cites the notation for arithmetic theta function. The Maass forms' analytic component is also described.

Chapter three of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It presents the techniques in obtaining the Shimura curves' cycles through modular form. It discusses the function of the Deligne-Mumford (DM) stack M in solving the moduli problem. Moreover, the Hodge bundle and uniformization's formulas are also discussed.

Chapter two of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It discusses the Deligne-Mumford stacks' arithmetic intersection theory, along with the one-dimensional case and green functions. It presents various formulations for arithmetic Chow groups. The formulas for Arakelov heights and pairing are also presented.

Chapter one of the book "Annals of Mathematics Studies: Modular Forms and Special Cycles on Shimura Curves," by Stephen S. Kudla, Michael Rapoport, and Tonghai Yang is presented. It discusses the geometric cycle of the Shimura M's arithmetic surface as well as the modular form in the nonholomorphic ellipsis. It denotes the formulations needed in obtaining Shimura curve through quadratic form and quarternion algebra. Information about the Einstein series is also discussed.