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1.

図書

図書
Michel L. Lapidus, Machiel van Frankenhuysen
出版情報: Boston : Birkhäuser, c2000  x, 268 p. ; 25 cm
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2.

図書

図書
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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3.

図書

図書
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
Andreas Juhl
出版情報: Basel ; Boston : Birkhauser Verlag, c2001  x, 709 p. ; 24 cm
シリーズ名: Progress in mathematics ; v. 194
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5.

図書

図書
Spencer J. Bloch
出版情報: Providence, R.I. : American Mathematical Society, c2000  ix, 97 p. ; 26 cm
シリーズ名: CRM monograph series ; v. 11
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目次情報: 続きを見る
Introduction
Tamagawa numbers
Continued Continuous cohomology
A theorem of Borel and its reformulation
The regulator map
The dilogarithm function The regulator map / I:
The regulator map and elliptic curves / II:
Elements in $K_2(E)$ of an elliptic curve $E$ A regulator formula
Bibliography
Index
Introduction
Tamagawa numbers
Continued Continuous cohomology
6.

図書

図書
Antanas Laurinčikas and Ramūnas Garunkštis
出版情報: Dordrecht : Kluwer Academic, c2002  viii, 189 p. ; 24 cm.
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目次情報: 続きを見る
Preface
Euler Gamma-Function / 1.:
Definition and Analytic Continuation / 1.1:
Representation by an Infinite Product / 1.2:
Functional Equation / 1.3:
Complementary Formula / 1.4:
Asymptotic Formulas / 1.5:
Hypergeometric Function / 1.6:
Notes
Definition of the Lerch Zeta-Function / 2.:
Analytic Continuation / 2.2:
Application of the Euler-Maclaurin Formula / 2.3:
Moments / 3.:
Approximation of L ([lambda], [alpha], s) by a Finite Sum / 3.1:
Montgomery-Vaughan Theorem / 3.2:
Mean Square of L ([lambda], [alpha], s) / 3.3:
Mean Square of L ([lambda], [alpha], s) with Respect to [alpha] / 3.4:
Approximate Functional Equation / 4.:
Proof of the Approximate Functional Equation / 4.1:
Application of the Approximate Functional Equation to the Mean Square of L ([lambda], [alpha], s) / 4.2:
Statistical Properties / 5.:
Limit Theorems on the Complex Plane / 5.1:
Limit Theorems in the Space of Analytic Functions / 5.2:
Joint Limit Theorems in the Space of Analytic Functions / 5.3:
Limit Theorems in the Space of Analytic Functions with Rational [alpha] / 5.4:
Universality / 6.:
Case of Transcendental [alpha] / 6.1:
Case of Rational [alpha] / 6.2:
Joint Universality of Lerch Zeta-Functions / 6.3:
Effectivization Problem of the Universality Theorem / 6.4:
Functional Independence / 7.:
The One-Dimensional Case / 7.1:
Joint Functional Independence / 7.2:
Distribution of Zeros / 8.:
Zero-Free Region on the Right / 8.1:
Zero-Free Regions on the Left / 8.2:
Number of Nontrivial Zeros / 8.3:
Estimates of the Number of Nontrivial Zeros / 8.4:
Sums over Nontrivial Zeros / 8.5:
References
Notation
Subject Index
Preface
Euler Gamma-Function / 1.:
Definition and Analytic Continuation / 1.1:
7.

図書

図書
Neal Koblitz
出版情報: New York ; Tokyo : Springer-Verlag, c1984  xii, 150 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 58
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目次情報: 続きを見る
p-adic numbers / 1:
p-adic interpolation of the Riemann zeta- function / 2:
Building up / 3:
p-adic power series / 4:
Rationality of the zeta-function of a set of equations over a finite field / 5:
p-adic numbers / 1:
p-adic interpolation of the Riemann zeta- function / 2:
Building up / 3:
8.

図書

図書
H. M. Edwards
出版情報: New York : Academic Press, 1974  xiii, 315 p ; 24 cm
シリーズ名: Pure and applied mathematics : a series of monographs and textbooks ; 58
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9.

図書

図書
S.J. Patterson
出版情報: Cambridge ; New York : Cambridge University Press, 1988  xiii, 156 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 14
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目次情報: 続きを見る
Historical introduction / 1:
The Poisson summation formula and the functional equation / 2:
The Hadamard product formula and 'explicit formulae' of prime number theory / 3:
The zeros of the zeta function and the prime number theorem / 4:
The Riemann hypothesis and the Lindel÷f hypothesis / 5:
The approximate functional equation / 6:
Appendix
Fourier theory
The Mellin transform
An estimate for certain integrals
The gamma function
Integral functions of finite order
Borel-Caratheodory theorems
Littlewood's theorem / 7:
Historical introduction / 1:
The Poisson summation formula and the functional equation / 2:
The Hadamard product formula and 'explicit formulae' of prime number theory / 3:
10.

図書

図書
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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