共查询到20条相似文献,搜索用时 15 毫秒
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Olav K. Richter 《Proceedings of the American Mathematical Society》2000,128(3):701-708
We define theta functions attached to indefinite quadratic forms over real number fields and prove that these theta functions are Hilbert modular forms by regarding them as specializations of symplectic theta functions. The eighth root of unity which arises under modular transformations is determined explicitly.
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Larry J. Gerstein 《Journal of Number Theory》1979,11(4):529-541
The isometry problem is studied for unimodular quadratic forms over the Hasse domains of global function fields. Over the polynomial ring k[x] the problem reduces to classification of forms over k; but examples are provided showing that in general no such reduction occurs, even when the underlying ring is Euclidean. Connections with the structure of the ideal class group are given, and a complete invariant for the isometry class is found in the ternary isotropic case. 相似文献
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W. C. Waterhouse 《Archiv der Mathematik》1986,47(3):229-231
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Martin Krüskemper 《manuscripta mathematica》1989,65(2):225-243
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT
L/F
()=1 andTr
L/F
(i)=i fori=2,...n. 相似文献
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Martin ech Dominik Lachman Josef Svoboda Magdalna Tinkov Kristýna Zemkov 《Mathematische Nachrichten》2019,292(3):540-555
The aim of this article is to study (additively) indecomposable algebraic integers of biquadratic number fields K and universal totally positive quadratic forms with coefficients in . There are given sufficient conditions for an indecomposable element of a quadratic subfield to remain indecomposable in the biquadratic number field K. Furthermore, estimates are proven which enable algorithmization of the method of escalation over K. These are used to prove, over two particular biquadratic number fields and , a lower bound on the number of variables of a universal quadratic forms. 相似文献
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An anisotropic quadratic form φ is called round if φ ?aφ whenever φ represents a nontrivially. All round forms over global fields are completely determined. A generalization of a round form, called a group form, is investigated over global fields. 相似文献
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Howard Skogman 《Results in Mathematics》2001,39(1-2):169-182
We define Jacobi forms over a totally real algebraic number field K and construct examples by first embedding the group and the space into the symplectic group and the symplectic upper half space respectively. Then symplectic modular forms are created and Jacobi forms arise by taking the appropriate Fourier coefficients. Also some known relations of Jacobi forms to vector valued modular forms over rational numbers are extended to totally real fields. 相似文献
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E. A. Kashina 《Journal of Mathematical Sciences》1988,43(5):2663-2669
Let K be the totally real field of algebraic numbers of degree n=[k2e] with the discriminant D=D(K); t=t(x1, ..., xs) a totally positive quadratic form of the determinant d>0 over the ring of integers from the field K; S4. Let be the number of representations over of the number m by the form a complete singular series. It is proved that for given s and n, there exists a constant c such that for N(d)>0 it is not true that for all m with m totally positive.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 68–77, 1986. 相似文献
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B. M. Kim 《Commentarii Mathematici Helvetici》2000,75(3):410-414
In this paper, we will prove there are infinitely many integers n such that n
2— 1 is square-free and admits universal octonary diagonal quadratic forms.
Received: November 2, 1998. 相似文献
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朱福祖 《中国科学A辑(英文版)》2001,44(1):7-14
Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of integers Rm of an imaginary quadratic field ℚ(√−m). Using our methods, one can construct explicitly an n-ary nondecomposable positive definite Hermitian Rm-lattice ( L, h) with given discriminant 2 for every n⩾2 (resp. n⩾13 or odd n⩾3) and square-free m = 12 k + t with k⩾1 and t∈ (1,7) (resp. k⩾1 and t = 2 or k⩾0 and t∈ 5,10,11). We study also the case for discriminant different from 2. 相似文献
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Masanari Kida. 《Mathematics of Computation》1999,68(228):1679-1685
The main result of this paper is that an elliptic curve having good reduction everywhere over a real quadratic field has a -rational point under certain hypotheses (primarily on class numbers of related fields). It extends the earlier case in which no ramification at is allowed. Small fields satisfying the hypotheses are then found, and in four cases the non-existence of such elliptic curves can be shown, while in three others all such curves have been classified.
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Werner Georg Nowak 《Archiv der Mathematik》2012,99(5):433-442
This article is concerned with Ramanujan sums ${c_{\mathcal{I}_1}(\mathcal{I}),}$ where ${\mathcal{I},\mathcal{I}_1}$ are integral ideals in an arbitrary quadratic number field ${\mathbb{Q}(\sqrt{d}).}$ In particular, the asymptotic behavior of sums of ${c_{\mathcal{I}_1}(\mathcal{I}),}$ over both ${\mathcal{I}}$ and ${c_{\mathcal{I}_1}(\mathcal{I}),}$ is investigated. 相似文献
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Let F be a field of characteristic different from 2 and let ø be an anisotropic 8-dimensional quadratic form over F with trivial deter-minant. We study the remaining open cases in the problem of describing the quadratic forms ψ such that ø becomes isotropic over the function field (ψ). 相似文献