scholarly journals On the 4-norm of an automorphic form

2013 ◽  
Vol 15 (5) ◽  
pp. 1825-1852 ◽  
Author(s):  
Valentin Blomer
Keyword(s):  
Automorphic Form

The Construction of Automorphic Forms From the Derivatives of a Given Form II

1985 ◽  
Vol 28 (3) ◽  
pp. 306-316
Author(s):  
R. A. Rankin
Keyword(s):  
Automorphic Form ◽  
Symmetric Functions ◽  
Automorphic Forms ◽  
Explicit Constructions ◽  
Derivatives Of

AbstractExplicit constructions of polynomials of preassigned degree and weight in the derivatives of a given automorphic form are described and studied, supplementing the results of an earlier paper. It turns out that the problem is essentially one concerning symmetric functions rather than automorphic forms.

Constructing an automorphic form from the orbit of a transformation

2007 ◽  
Vol 48 (5) ◽  
pp. 769-777
Author(s):  
E. P. Aksent’eva ◽  
F. N. Garif’yanov
Keyword(s):  
Automorphic Form

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.

An automorphic form of Ando's theorem

1989 ◽  
Vol 12 (3) ◽  
pp. 424-434 ◽  
Author(s):  
Kuen-Shan Ling ◽  
Paul S. Muhly
Keyword(s):  
Automorphic Form

scholarly journals RANKIN–COHEN TYPE DIFFERENTIAL OPERATORS FOR SIEGEL MODULAR FORMS

1998 ◽  
Vol 09 (04) ◽  
pp. 443-463 ◽  
Author(s):  
WOLFGANG EHOLZER ◽  
TOMOYOSHI IBUKIYAMA
Keyword(s):  
Half Space ◽  
Modular Forms ◽  
Automorphic Form ◽  
Differential Operators ◽  
Automorphic Forms ◽  
Siegel Modular Forms ◽  
Elliptic Case ◽  
Vector Valued

Let ℍn be the Siegel upper half space and let F and G be automorphic forms on ℍn of weights k and l, respectively. We give explicit examples of differential operators D acting on functions on ℍn × ℍn such that the restriction of [Formula: see text] to Z = Z1 = Z2 is again an automorphic form of weight k + l + v on ℍn. Since the elliptic case, i.e. n = 1, has already been studied some time ago by R. Rankin and H. Cohen we call such differential operators Rankin–Cohen type operators. We also discuss a generalisation of Rankin–Cohen type operators to vector valued differential operators.

scholarly journals Periods of automorphic forms: the case of

2014 ◽  
Vol 151 (4) ◽  
pp. 665-712 ◽  
Author(s):  
Atsushi Ichino ◽  
Shunsuke Yamana
Keyword(s):  
Automorphic Form ◽  
Automorphic Forms ◽  
Selberg Integral ◽  
Selberg Integrals ◽  
Diagonal Subgroup ◽  
Periods Of Automorphic Forms

Following Jacquet, Lapid and Rogawski, we define a regularized period of an automorphic form on $\text{GL}_{n+1}\times \text{GL}_{n}$ along the diagonal subgroup $\text{GL}_{n}$ and express it in terms of the Rankin–Selberg integral of Jacquet, Piatetski-Shapiro and Shalika. This extends the theory of Rankin–Selberg integrals to all automorphic forms on $\text{GL}_{n+1}\times \text{GL}_{n}$.

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 Electric fields on a surface of constant negative curvature

2000 ◽  
Vol 20 (3) ◽  
pp. 681-696 ◽  
Author(s):  
F. BONETTO ◽  
G. GENTILE ◽  
V. MASTROPIETRO
Keyword(s):  
Electric Fields ◽  
Continuous Time ◽  
Automorphic Form ◽  
Negative Curvature ◽  
Contraction Rate ◽  
Average Volume ◽  
Constant Negative Curvature ◽  
Volume Contraction ◽  
Large Fluctuations ◽  
Anosov Flows

A one-parameter family of time reversible Anosov flows is studied; physically, it describes a particle moving on a surface of constant negative curvature under the action of an electric field (corresponding to an automorphic form) and of a ‘thermostatting’ force (given by Gauss's least-constraint principle). We show that the flows are dissipative, in the sense that the average volume contraction rate is positive and the Sinai–Ruelle–Bowen measure is singular with respect to the volume: therefore they verify the assumptions for the validity of the continuous time version of Gallavotti–Cohen's fluctuation theorem for the large fluctuations of the average volume contraction rate. If several independent electric fields are considered, it makes sense to ask for the validity of Onsager's reciprocity: we show, by explicitly computing the relevant transport coefficents, that it is indeed obeyed.

An $$\widehat{A_4 }$$ extension of ? attached to a non-selfdual automorphic form onGL(3)

1991 ◽  
Vol 291 (1) ◽  
pp. 753-766 ◽  
Author(s):  
Avner Ash ◽  
Richard Pinch ◽  
Richard Taylor
Keyword(s):  
Automorphic Form
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