Hilbert Modular Forms

Freitag, Eberhard

doi:10.1007/978-3-662-02638-0_2

Cited by 85 publications

(212 citation statements)

References 0 publications

Supporting

Mentioning

204

Contrasting

Unclassified

Order By: Relevance

“…In string theory, scattering amplitudes are given perturbatively at loop order h by the moments of a measure on the moduli space of Riemann surfaces of genus h. For example, the vacuum-to-vacuum amplitude, or cosmological constant, is given by an expression of the form This correspondence between the superstring measure and modular forms is particularly simple at one-loop, where dµ[δ] ∼ ϑ[δ](0, Ω) 4 /η(Ω) 12 , so that dµ [δ](Ω) is essentially a ϑ-constant. No such simple relation is known in general.…”

Section: Introductionmentioning

confidence: 99%

Asyzygies, modular forms, and the superstring measure II

D’Hoker

Phong

2005

Nuclear Physics B

View full text Add to dashboard Cite

The goal of this paper and of a subsequent continuation is to find some viable ansatze for the three-loop superstring chiral measure. For this, two alternative formulas are derived for the two-loop superstring chiral measure. Unlike the original formula, both alternates admit modular covariant generalizations to higher genus. One of these two generalizations is analyzed in detail in the present paper, with the analysis of the other left to the next paper of the series.

show abstract

Section: Introductionmentioning

confidence: 99%

Asyzygies, modular forms, and the superstring measure II

D’Hoker

Phong

2005

Nuclear Physics B

View full text Add to dashboard Cite

show abstract

“…In particular, the interior motive then coincides with the e-part of the motive of the (open) Kuga-Sato variety. This can be seen as a motivic explanation of [F,Rem. I.4.8]: "If f is a modular form, but not a cusp form, then r 1 = .…”

Section: 2]mentioning

confidence: 92%

On the Interior Motive of Certain Shimura Varieties: the Case of Hilbert-Blumenthal varieties

Wildeshaus¹

2011

International Mathematics Research Notices

View full text Add to dashboard Cite

show abstract

“…In other words, F j is a Hilbert modular form of weight k on the kernel of ρ. By [Fre90,Prop. 4.9] the F j satisfy the Köcher principle (loc.…”

Section: Jacobi Forms As Vector-valued Hilbert Modular Formsmentioning

confidence: 99%

Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields

Boylan

2015

Lecture Notes in Mathematics

View full text Add to dashboard Cite

In analogy to the theory of classical Jacobi forms which has proven to have various important applications ranging from number theory to physics, we develop in this thesis a theory of Jacobi forms over arbitrary totally real number fields. For this end we need to develop, first of all, a theory of finite quadratic modules over number fields and their associated Weil representations. As a main application of our theory, we are able to describe explicitly all singular Jacobi forms over arbitrary totally real number fields whose indices have rank 1. We expect that these singular Jacobi forms play a similar important role in this new founded theory of Jacobi forms over number fields as the Weierstrass sigma function does in the classical theory of Jacobi forms. ZusammenfassungIn Analogie zur klassischen Theorie der Jacobiformen, die viele wichtige Anwendungen in der Zahlentheorie bis hin zur Physik hat, entwickeln wir in der vorliegenden Arbeit eine Theorie der Jacobiformenüber total reellen Zahlkörpern. Hierzu müssen wir zunächst eine Theorie endlich quadratischer Modulnüber Zahlkörpern und ihrer zugehörigen Weil-Darstellungen entwickeln. Als eine Hauptanwendung der hier entwickelten Theorie sind wir in der Lage, alle singulären Jacobiformenüber beliebigen total reellen Zahlkörpern, deren Indizes Gitter vom Rang 1 sind, explizit zu beschreiben. Wir gehen davon aus, dass diese singulären Jacobiformen eineähnlich wichtige Rolle in der hier begründeten Theorie der Jacobiformenüber Zahlkörpern spielen werden wie es von der Weierstaßschen sigma-Funktion in der klassischen Theorie der Jacobiformen her bekannt ist.To my beloved father, Mustafa Boylan

show abstract

Hilbert Modular Forms

Cited by 85 publications

References 0 publications

Asyzygies, modular forms, and the superstring measure II

Asyzygies, modular forms, and the superstring measure II

On the Interior Motive of Certain Shimura Varieties: the Case of Hilbert-Blumenthal varieties

Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields

Contact Info

Product

Resources

About