Period integrals of Kudla-Millson lifts and L-functions associated to vector valued modular forms

Metzler, Ingmar (2024)
Period integrals of Kudla-Millson lifts and L-functions associated to vector valued modular forms.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00028711
Ph.D. Thesis, Primary publication, Publisher's Version

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Item Type:

Ph.D. Thesis

Type of entry:

Primary publication

Title:

Period integrals of Kudla-Millson lifts and L-functions associated to vector valued modular forms

Language:

English

Referees:

Bruinier, Prof. Dr. Jan Hendrik ; Scheithauer, Prof. Dr. Nils

Date:

18 November 2024

Place of Publication:

Darmstadt

Collation:

xv, 377 Seiten

Date of oral examination:

15 October 2024

DOI:

10.26083/tuprints-00028711

Abstract:

The present thesis establishes a new converse theorem for Borcherds products. Moreover, the injectivity of the Kudla–Millson theta lift is demonstrated in the O(n,2) case in greater generality than is currently available in the literature. Both results are derived under the assumption of a single hyperbolic split of the base lattice. Additionally, symmetric square type L-series associated to elliptic vector valued modular forms are examined and special values of these series are linked to cycle integrals of Kudla–Millson liftings.

Alternative Abstract:

Alternative Abstract

Language

In der vorliegenden Arbeit wird ein neuer Umkehrsatz für Borcherdsprodukte bewiesen. Außerdem wird die Injektivität des Kudla–Millsons lifts im O(n,2) Fall in größerer Allgemeinheit nachgewiesen als die aktuelle Literaturlage belegt. Beide Resultate werden unter der Annahme eines einzigen hyperbolischen Splits des zu Grunde liegenden Gitters gezeigt. Zusätzlich werden L-Reihen vom „symmetric square“ Typ, welche zu vektorwertigen Modulformen assoziiert werden, untersucht und spezielle Werte derselben mit Zykelintegralen von Kudla–Millson lifts in Verbindung gebracht.

German

Uncontrolled Keywords:

Borcherds products, Cycle integrals, Automorphic lifts, Kudla-Millson theta correspondence, L-series, Theta lifts

Status:

Publisher's Version

URN:

urn:nbn:de:tuda-tuprints-287116

Classification DDC:

500 Science and mathematics > 510 Mathematics

Divisions:

04 Department of Mathematics > Algebra > Automorphic Forms, Number Theory, Algebraic Geometry

Date Deposited: