The Maaß space on the half-plane of Cayley numbers of degree two

Eie, Minking; Krieg, Aloys

doi:10.1007/bf02571786

Cited by 14 publications

(17 citation statements)

References 17 publications

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“…This result also coincides with Karel [37]. They have an inessential error of a numerical factor which has been pointed out in [21]. …”

Section: C4 Densities At Infinite Placessupporting

confidence: 89%

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Back Matter

2008

Monographs in Number Theory

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“…This result also coincides with Karel [37]. They have an inessential error of a numerical factor which has been pointed out in [21]. …”

Section: C4 Densities At Infinite Placessupporting

confidence: 89%

“…In view of the fact that the theta series h∈O 2 e 2πi(h t h,Z) is a modular form of weight 4 on H 2 [21], it is plausible that the expression…”

Section: C2 Interpretations As Densitiesmentioning

confidence: 99%

Back Matter

2008

Monographs in Number Theory

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“…In order to quantize this system we rewrite the 320 real gravitino components ϕ a α in terms of 160 complex ones according tõ ϕ a A := ϕ a A + iϕ a A+16 (32) for A, B, .. = 1, . .…”

Section: Supersymmetrymentioning

confidence: 99%

Cosmological quantum billiards

Kleinschmidt

Nicolai

2012

Foundations of Space and Time

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The mini-superspace quantization of D = 11 supergravity is equivalent to the quantization of a E 10 /K(E 10 ) coset space sigma model, when the latter is restricted to the E 10 Cartan subalgebra. As a consequence, the wavefunctions solving the relevant mini-superspace Wheeler-DeWitt equation involve automorphic (Maass wave) forms under the modular group W + (E 10 ) ∼ = P SL 2 (O). Using Dirichlet boundary conditions on the billiard domain a general inequality for the Laplace eigenvalues of these automorphic forms is derived, entailing a wave function of the universe that is generically complex and always tends to zero when approaching the initial singularity. The significance of these properties for the nature of singularities in quantum cosmology in comparison with other approaches is discussed. The present approach also offers interesting new perspectives on some long standing issues in canonical quantum gravity.

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“…Examples of functions in Jk,m(") are given by the Fourier-Jacobi coefficients of modular forms on the half-plane of the Cayley numbers of degree 2 (cf. [6]). …”

Section: Notationsmentioning

confidence: 99%

“…j=o The 8x8 matrix S = (<r(a,, a,-)) is positive definite, even and unimodular (cf. [6]). In the notation of [10, p. 101], we therefore have ûm,q(z,w) = &g,mSw/m(z, mS;Zs).…”

Section: Theta Seriesmentioning

confidence: 99%