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91.
The eigenvalues of a differential operator on a Hilbert-Pόlya space are determined. It is shown that these eigenvalues are exactly the nontrivial zeros of the Riemann $\zeta$-function. Moreover, their corresponding multiplicities are the same. 相似文献
92.
93.
The topological zeta function and Igusa's local zeta functionare respectively a geometrical invariant associated to a complexpolynomial f and an arithmetical invariant associated to a polynomialf over a p-adic field. When f is a polynomial in two variables we prove a formula forboth zeta functions in terms of the so-called log canonicalmodel of f-1{0} in A2. This result yields moreover a conceptualexplanation for a known cancellation property of candidate polesfor these zeta functions. Also in the formula for Igusa's localzeta function appears a remarkable non-symmetric q-deformationof the intersection matrix of the minimal resolution of a Hirzebruch-Jungsingularity. 1991 Mathematics Subject Classification: 32S5011S80 14E30 (14G20) 相似文献
94.
Emmanuel Tollis. 《Mathematics of Computation》1997,66(219):1295-1321
In this paper, we describe a computation which established the GRH to height (resp. ) for cubic number fields (resp. quartic number fields) with small discriminant. We use a method due to E. Friedman for computing values of Dedekind zeta functions, we take care of accumulated roundoff error to obtain results which are mathematically rigorous, and we generalize Turing's criterion to prove that there is no zero off the critical line. We finally give results concerning the GRH for cubic and quartic fields, tables of low zeros for number fields of degree and , and statistics about the smallest zero of a number field.
95.
Zeta Function on a Generalised Cone 总被引:2,自引:0,他引:2
The analytic properties of the -function for a Laplace operator on a generalised cone
are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential. 相似文献
96.
We study the relations between different determinants of the Dirac operator over a manifold with boundary considered as sections of a holomorphic line bundle over the Grassmannian of boundary conditions of Atiyah–Patodi–Singer type. 相似文献
97.
The continuity of the hyperbolic zeta function of lattices
H
(¦),=+it, >1, as a function on the metric space of lattices is proved.Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 522–526, April, 1998.The authors wish to express their gratitude to Professor N. M. Korobkov and Professor V. I. Nechaev for fruitful discussions. 相似文献
98.
Formulas for calculating the sum of singular series corresponding to the number of representations of integers by some quadratic forms in 12 variables with integral coefficient are derived. 相似文献
99.
Jangheon Oh 《Transactions of the American Mathematical Society》1998,350(9):3639-3655
We study the relation between zeta-functions and Iwasawa modules. We prove that the Iwasawa modules for almost all determine the zeta function when is a totally real field. Conversely, we prove that the -part of the Iwasawa module is determined by its zeta-function up to pseudo-isomorphism for any number field Moreover, we prove that arithmetically equivalent CM fields have also the same -invariant.
100.
Raf Cluckers 《Journal of Number Theory》2008,128(7):2185-2197
In [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105-114], it is shown that a p-adic semi-algebraic set can be partitioned in such a way that each part is semi-algebraically isomorphic to a Cartesian product where the sets R(k) are very basic subsets of Qp. It is suggested in [R. Cluckers, Classification of semi-algebraic sets up to semi-algebraic bijection, J. Reine Angew. Math. 540 (2001) 105-114] that this result can be adapted to become useful to p-adic integration theory, by controlling the Jacobians of the occurring isomorphisms. In this paper we show that the isomorphisms can be chosen in such a way that the valuations of their Jacobians equal the valuations of products of coordinate functions, hence obtaining a kind of explicit p-adic resolution of singularities for semi-algebraic p-adic functions. We do this by restricting the used isomorphisms to a few specific types of functions, and by controlling the order in which they appear. This leads to an alternative proof of the rationality of the Poincaré series associated to the p-adic points on a variety, as proven by Denef in [J. Denef, The rationality of the Poincaré series associated to the p-adic points on a variety, Invent. Math. 77 (1984) 1-23]. 相似文献