Construction of Automorphic Forms for Ample Factors of Quasi-Abelian Varieties

Abe, Yukitaka

doi:10.2206/kyushujm.57.51

Cited by 3 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Looking for the non-cocompact case (i.e. Γ of rank r; 0 ≤ r < 2g) is therefore strongly motivated under a lot of different viewpoints (see [2,1,7] for example and references therein). However, the explicit construction of the holomorphic automorphic functions using Fourier series is still far from being understood in the general case of 0 ≤ r < 2g, except for r = 0 and r = 1.…”

Section: Introductionmentioning

confidence: 99%

On holomorphic theta functions associated to rank $r$ isotropic discrete subgroups of a $g$-dimensional complex space

Ghanmi,

Intissar,

Ainin

2015

Preprint

View full text Add to dashboard Cite

We are interested in the L 2 -holomorphic automorphic functions on a gdimensional complex space V g C endowed with a positive definite hermitian form and associated to isotropic discrete subgroups Γ of rank 2 ≤ r ≤ g. We show that they form an infinite reproducing kernel Hilbert space which looks like a tensor product of a theta Fock-Bargmann space on V r C = Span C (Γ) and the classical Fock-Bargmann space on V g−r C . Moreover, we provide an explicit orthonormal basis using Fourier series and we give the expression of its reproducing kernel function in terms of Riemann theta function of several variables with special characteristics.

show abstract

Section: Introductionmentioning

confidence: 99%

On holomorphic theta functions associated to rank $r$ isotropic discrete subgroups of a $g$-dimensional complex space

Ghanmi,

Intissar,

Ainin

2015

Preprint

View full text Add to dashboard Cite

show abstract

On holomorphic theta functions associated with rank r isotropic discrete subgroups

2022

View full text Add to dashboard Cite

ON QUASI-ABELIAN VARIETIES OF KIND k

Abe¹,

Umeno²

2006

Kyushu J. Math.

Self Cite

View full text Add to dashboard Cite

Abstract. Gherardelli and Andreotti defined a quasi-abelian variety of kind k. However, this definition is somewhat vague and we do not know the real meaning of the 'kind'. We give an example of a quasi-abelian variety which is of kind k > 0 but not of kind 0, in the sense of Gherardelli and Andreotti. We prove that if a quasiabelian variety X = C n / has an ample Riemann form of kind k, then it has an ample Riemann form of kind k for any k with 2k 2k n − m, where rank = n + m. Next we consider the pair (X, L) of a quasi-abelian variety X and a positive line bundle L on it. We characterize an extendable line bundle L to a compactification X of X.

show abstract

Construction of Automorphic Forms for Ample Factors of Quasi-Abelian Varieties

Cited by 3 publications

References 11 publications

On holomorphic theta functions associated to rank $r$ isotropic discrete subgroups of a $g$-dimensional complex space

On holomorphic theta functions associated to rank $r$ isotropic discrete subgroups of a $g$-dimensional complex space

On holomorphic theta functions associated with rank r isotropic discrete subgroups

ON QUASI-ABELIAN VARIETIES OF KIND k

Contact Info

Product

Resources

About