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1.

図書
図書
1. Groups acting on hyperbolic space : harmonic analysis and number theory
J. Elstrodt, F. Grunewald, J. Mennicke
出版情報: Berlin ; New York : Springer, 1998  xv, 524 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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2.

図書
図書
2. Spectral theory of the Riemann zeta-function
Yoichi Motohashi
出版情報: Cambridge : Cambridge University Press, 1997  ix, 228 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 127
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目次情報: 続きを見る
Non-Euclidean harmonics / 1：
Trace formulas / 2：
Automorphic L-functions / 3：
An explicit formula / 4：
Asymptotics / 5：
References
Index
Non-Euclidean harmonics / 1：
Trace formulas / 2：
Automorphic L-functions / 3：
3.

図書
図書
3. Random matrices, Frobenius eigenvalues, and monodromy
Nicholas M. Katz, Peter Sarnak
出版情報: Providence, R.I. : American Mathematical Society, c1999  xi, 419 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 45
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4.

図書
図書
4. The semi-simple zeta function of quaternionic Shimura varieties
Harry Reimann
出版情報: Berlin ; New York : Springer-Verlag, c1997  143 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1657
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5.

図書
図書
5. Area, lattice points, and exponential sums
M.N. Huxley
出版情報: Oxford : Clarendon Press , New York : Oxford University Press, 1996  xii, 494 p. ; 24 cm
シリーズ名: London Mathematical Society monographs ; new ser., no. 13
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6.

図書
図書
6. Selberg zeta and theta functions : a differential operator approach
Ulrich Bunke, Martin Olbrich
出版情報: Berlin : Akademie Verlag , New York : VCH, c1995  168 p. ; 24 cm
シリーズ名: Mathematical research = Mathematische Forschung ; v. 83
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目次情報: 続きを見る
From Wave Equation to Trace Formula
Singularities of the Theta Function
A Determinant Representation of the Selberg Zeta Function
The Functional Equations of Selberg and Ruellezeta Functions
Dirac Operators and Form Laplacians
From Wave Equation to Trace Formula
Singularities of the Theta Function
A Determinant Representation of the Selberg Zeta Function
7.

図書
図書
7. Non-Archimedean L-functions of Siegel and Hilbert modular forms (: gw ; : us)
Alexey A. Panchishkin
出版情報: Berlin ; Tokyo : Springer-Verlag, c1991  157 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1471
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8.

図書
図書
8. The Riemann zeta-function
by A.A. Karatsuba, S.M. Voronin ; translated from the Russian by Neal Koblitz
出版情報: Berlin ; New York : Walter de Gruyter, 1992  xii, 396 p. ; 25 cm
シリーズ名: De Gruyter expositions in mathematics ; 5
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9.

図書
図書
9. Algebraic curves over finite fields
Carlos Moreno
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1991  ix, 246 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 97
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目次情報: 続きを見る
Preface
Algebraic curves and function fields / 1：
Geometric aspects / 1.1：
Introduction / 1.1.1：
Affine varieties / 1.1.2：
Projective varieties / 1.1.3：
Morphisms / 1.1.4：
Rational maps / 1.1.5：
Non-singular varieties / 1.1.6：
Smooth models of algebraic curves / 1.1.7：
Algebraic aspects / 1.2：
Points on the projective line P[superscript 1] / 1.2.1：
Extensions of valuation rings / 1.2.3：
Points on a smooth curve / 1.2.4：
Independence of valuations / 1.2.5：
Exercises
Notes
The Riemann-Roch theorem / 2：
Divisors / 2.1：
The vector space L(D) / 2.2：
Principal divisors and the group of divisor classes / 2.3：
The Riemann theorem / 2.4：
Pre-adeles (repartitions) / 2.5：
Pseudo-differentials (the Riemann-Roch theorem) / 2.6：
Zeta functions / 3：
The zeta functions of curves / 3.1：
The functional equation / 3.3：
Consequences of the functional equation / 3.3.1：
The Riemann hypothesis / 3.4：
The L-functions of curves and their functional equations / 3.5：
Preliminary remarks and notation / 3.5.1：
Exponential sums / 3.5.2：
The zeta function of the projective line / 4.1：
Gauss sums: first example of an L-function for the projective line / 4.2：
Properties of Gauss sums / 4.3：
Cyclotomic extensions: basic facts / 4.3.0：
Elementary properties / 4.3.1：
The Hasse-Davenport relation / 4.3.2：
Stickelberger's theorem / 4.3.3：
Kloosterman sums / 4.4：
Second example of an L-function for the projective line / 4.4.1：
A Hasse-Davenport relation for Kloosterman sums / 4.4.2：
Third example of an L-function for the projective line / 4.5：
Basic arithmetic theory of exponential sums / 4.6：
Part I: L-functions for the projective line / 4.6.1：
Part II: Artin-Schreier coverings / 4.6.2：
The Hurwitz-Zeuthen formula for the covering [pi]: C [right arrow] C / 4.6.3：
Goppa codes and modular curves / 5：
Elementary Goppa codes / 5.1：
The affine and projective lines / 5.2：
Affine line A[superscript 1](k) / 5.2.1：
Projective line P[superscript 1] / 5.2.2：
Goppa codes on the projective line / 5.3：
Algebraic curves / 5.4：
Separable extensions / 5.4.1：
Closed points and their neighborhoods / 5.4.2：
Differentials / 5.4.3：
The theorems of Riemann-Roch, of Hurwitz and of the Residue / 5.4.4：
Linear series / 5.4.6：
Algebraic geometric codes / 5.5：
Algebraic Goppa codes / 5.5.1：
Codes with better rates than the Varshamov-Gilbert bound / 5.5.2：
The theorem of Tsfasman, Vladut and Zink / 5.6：
Modular curves / 5.6.1：
Elliptic curves over C / 5.6.2：
Elliptic curves over the fields F[subscript p], Q / 5.6.3：
Torsion points on elliptic curves / 5.6.4：
Igusa's theorem / 5.6.5：
The modular equation / 5.6.6：
The congruence formula / 5.6.7：
The Eichler-Selberg trace formula / 5.6.8：
Proof of the theorem of Tsfasman, Vladut and Zink / 5.6.9：
Examples of algebraic Goppa codes / 5.7：
The Hamming (7,4) code / 5.7.1：
BCH codes / 5.7.2：
The Fermat cubic (Hermite form) / 5.7.3：
Elliptic codes (according to Driencourt-Michon) / 5.7.4：
The Klein quartic / 5.7.5：
Simplification of the singularities of algebraic curves / Appendix：
Homogeneous coordinates in the plane / A.1：
Basic lemmas / A.2：
Dual curves / A.3：
Plucker formulas / A.3.1：
Quadratic transformations / A.4：
Quadratic transform of a plane curve / A.4.1：
Quadratic transform of a singularity / A.4.2：
Singularities off the exceptional lines / A.4.3：
Reduction of singularities / A.4.4：
Bibliography
Index
Preface
Algebraic curves and function fields / 1：
Geometric aspects / 1.1：
10.

図書
図書
10. Explicit formulas for regularized products and series (: gw ; : us)
Jay Jorgenson & Serge Lang, Dorian Goldfeld
出版情報: Berlin ; New York : Springer-Verlag, c1994  viii, 154 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1593 . Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn ; vol. 21
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目次情報:
Explicit formulas for regularized products and series / Jay Jorgenson and Serge Lang
A Spectral interpretation of Weil's explicit formula / Dorian Goldfeld
Explicit formulas for regularized products and series / Jay Jorgenson and Serge Lang
A Spectral interpretation of Weil's explicit formula / Dorian Goldfeld
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