scholarly journals On standard L-functions attached to automorphic forms on definite orthogonal groups

1998 ◽  
Vol 152 ◽  
pp. 57-96 ◽  
Author(s):  
Atsushi Murase ◽  
Takashi Sugano
Keyword(s):  
Functional Equation ◽  
Number Field ◽  
Algebraic Number ◽  
Orthogonal Group ◽  
Automorphic Form ◽  
Automorphic Forms ◽  
Algebraic Number Field ◽  
Constant Function ◽  
Orthogonal Groups ◽  
Totally Real

Abstract.We show an explicit functional equation of the standard L-function associated with an automorphic form on a definite orthogonal group over a totally real algebraic number field. This is a completion and a generalization of our previous paper, in which we constructed standard L-functions by using Rankin-Selberg convolution and the theory of Shintani functions under certain technical conditions. In this article we remove these conditions. Furthermore we show that the L-function of f has a pole at s = m/2 if and only if f is a constant function.

scholarly journals Automorphy factors for a Hilbert modular group

1988 ◽  
Vol 30 (2) ◽  
pp. 231-236
Author(s):  
Shigeaki Tsuyumine
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Rational Number ◽  
Modular Group ◽  
Algebraic Number Field ◽  
Maximal Order ◽  
Hilbert Modular Group ◽  
Hilbert Modular ◽  
Totally Real

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = ℚ(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group.

scholarly journals Theta series liftings from orthogonal groups to semi-simple groups

2000 ◽  
Vol 69 (1) ◽  
pp. 127-142
Author(s):  
Min Ho Lee
Keyword(s):  
Half Space ◽  
Lie Group ◽  
Orthogonal Group ◽  
Automorphic Form ◽  
Automorphic Forms ◽  
Theta Series ◽  
Symmetric Domain ◽  
Simple Groups ◽  
Orthogonal Groups ◽  
Spin Groups

AbstractWe study a correspondence between automorphic forms on an orthogonal group and automorpbic forms on a semi-simple Lie group associated to an equivariant holomorphic map of a symmetric domain into a Siegel upper half space. We construct an automorphic form on the symmetric domain thatg corresponds to an automorphic form on an orthogonal group using theta series, and prove that such a correspondence is compatible with the appropriate Hecks operator actions on the corresponding automorphic forms. As an example, we describe the case of spin groups.

scholarly journals Scalar extension of quadratic lattices II

1977 ◽  
Vol 67 ◽  
pp. 159-164 ◽  
Author(s):  
Yoshiyuki Kitaoka
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Rational Numbers ◽  
Positive Definite ◽  
Maximal Order ◽  
Quadratic Space ◽  
Quadratic Lattices ◽  
Totally Real ◽  
Quadratic Lattice

Let k be a totally real algebraic number field, the maximal order of k, and let L (resp. M) be a Z-lattice of a positive definite quadratic space U (resp. V) over the field Q of rational numbers. Suppose that there is an isometry σ from L onto M. We have shown that the assumption implies σ(L) = M in some cases in [2]. Our aim in this paper is to improve the results of [2]. In § 1 we introduce the notion of E-type: Let L be a positive definite quadratic lattice over Z.

scholarly journals On the class number of a unit lattice over a ring of real quadratic integers

1983 ◽  
Vol 92 ◽  
pp. 89-106 ◽  
Author(s):  
Yoshio Mimura
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Class Number ◽  
Orthonormal Basis ◽  
Algebraic Number Field ◽  
Positive Definite ◽  
Quadratic Space ◽  
Totally Real ◽  
Real Quadratic

Let K be a totally real algebraic number field. In a positive definite quadratic space over K a lattice En is called a unit lattice of rank n if En has an orthonormal basis {e1 …, en}. The class number one problem is to find n and K for which the class number of En is one. Dzewas ([1]), Nebelung ([3]), Pfeuffer ([6], [7]) and Peters ([5]) have settled this problem.

On correspondence between orders and ideals with a normal basis in cyclic subfields of Q(ξp) of a prime degree l

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Juraj Kostra
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Normal Basis ◽  
Prime Degree ◽  
One To One

AbstractLet K be a tamely ramified cyclic algebraic number field of prime degree l. In the paper one-to-one correspondence between all orders of K with a normal basis and all ideals of K with a normal basis is given.

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