## Collected Papers III: 1978–1988In 1996 the AMS awarded Goro Shimura the Steele Prize for Lifetime Achievement for his "important and extensive work on arithmetical geometry and automorphic forms." His seminal work has resulted in the "many notations in number theory that carry his name and that have long been familiar to workers in the field." These 5 volumes contain 103 of his most important papers, beginning in 1954 and continuing up through the present. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

List of Articles | vii |

78a On certain reciprocitylaws for theta functions and modular forms 1 | 51 |

78b The arithmetic of automorphic forms with respect to a unitary group 38 | 38 |

78c The special values of the zeta functions associated with Hilbert | 75 |

79a Automorphic forms and the periods of abelian varieties | 115 |

79b On some problems of algebraicity | 147 |

80 The arithmetic of certain zeta functions and automorphic forms | 154 |

8la The critical values of certain zeta functions associated with modular | 217 |

83a Algebraic relations between critical values of zeta functions | 422 |

83b On Eisenstein series | 455 |

84a Differential operators and the singular values of Eisenstein series 515 | 584 |

85a On Eisenstein series of halfintegral weight | 610 |

85b On the Eisenstein series of Hilbert modular groups | 644 |

86 On a class of nearly holomorphic automorphic forms | 686 |

87a Nearly holomorphic functions on hermitian symmetric spaces | 746 |

87b On Hilbert modular forms of halfintegral weight | 774 |

The case of automorphic forms on a quaternion algebra | 279 |

82a Models of an abelian variety with complex multiplication over | 349 |

82b The periods of certain automorphic forms of arithmetic type | 360 |

82c Confluent hypergeometric functions on tube domains | 388 |

88 On the critical values of certain Dirichlet series and the periods | 848 |

Notes II | 909 |

### Other editions - View all

### Common terms and phrases

a e G abelian varieties algebraic number field arithmetic assume automorphic forms belongs CM-field CM-point CM-type completes the proof congruence subgroup consider constant convergent cusp form denote differential operators domain easily eigenvalues Eisenstein series embedding fact factor of automorphy finite index formula Fourier coefficients Fourier expansion fractional ideal function f given half-integral weight Hecke character Hecke operators hence hermitian Hilbert modular forms holomorphic functions implies integral ideal integral weight irreducible isomorphism lattice Lemma Let f linear Math matrix meromorphic function modulo Moreover multiple nearly holomorphic nonzero notation Observe orthogonal polynomial positive integer primitive proof of Theorem Proposition 3.1 prove Q-rational elements Re(s representation residue resp result satisfying Section set of representatives Shimura shows simple pole subfield subgroup F subset subspace Suppose symmetric Theorem 3.2 theta values vector space zeta functions