Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors

Bruinier, Jan Hendrik

doi:10.1007/b83278

Cited by 303 publications

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“…As a consequence, we obtain the following converse theorem for the Borcherds lift (see [Br1], [Br2] Chapter 5).…”

Section: Automorphic Green Functionsmentioning

confidence: 80%

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Hilbert Modular Forms and Their Applications

Bruinier

2008

The 1-2-3 of Modular Forms

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“…As a consequence, we obtain the following converse theorem for the Borcherds lift (see [Br1], [Br2] Chapter 5).…”

Section: Automorphic Green Functionsmentioning

confidence: 80%

“…So far it is only known for particular arithmetic subgroups of O(2, n), see [Br2], [Br3]. For example, if we go to congruence subgroups of the Hilbert modular group Γ F , it is not clear whether the analogue of Theorem 3.31 holds or not.…”

Section: Automorphic Green Functionsmentioning

confidence: 99%

Hilbert Modular Forms and Their Applications

Bruinier

2008

The 1-2-3 of Modular Forms

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“…Zwegers's thesis has sparked a flurry of recent activity involving such Maass forms. Indeed, harmonic Maass forms are now known to play a central role in the study of Ramanujan's mock theta functions, as well as other important mathematical topics: Borcherds products, derivatives of modular L-functions, GrossZagier formulas and Faltings heights of CM cycles, partitions,and traces of singular moduli (see Bringmann and Ono [5;6], Bringmann, Ono and Rhoades [7], Bruinier [8], Bruinier and Funke [9], Bruinier and Ono [10], Bruinier and Yang [12], Ono [40], Zagier [55] and Zwegers [56]). …”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

SO(3)–Donaldson invariants of ℂP²and mock theta functions

Malmendier

Ono

2012

Geom. Topol.

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We compute the Moore-Witten regularized u-plane integral on CP 2 , and we confirm the conjecture that it is the generating function for the SO.3/-Donaldson invariants of CP 2 . We also derive generating functions for the SO.3/-Donaldson invariants with 2N f massless monopoles using the geometry of certain rational elliptic surfaces (N f 2 f0; 2; 3; 4g), and we show that the partition function for N f D 4 is nearly modular. Our results rely heavily on the theory of mock theta functions and harmonic Maass forms (for example, see Ono [40]). 57R57

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“…Moreover, by [7,Prop. 4.5], it follows that the Laplace operators on the Kudla-Millson theta kernel are related by .17) 2.5.…”

Section: The Kudla-millson Theta Functionsmentioning

confidence: 96%

Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

Bruinier

Ono

2013

Advances in Mathematics

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Abstract. We prove that the coefficients of certain weight −1/2 harmonic Maass forms are "traces" of singular moduli for weak Maass forms. To prove this theorem, we construct a theta lift from spaces of weight −2 harmonic weak Maass forms to spaces of weight −1/2 vectorvalued harmonic weak Maass forms on Mp 2 (Z), a result which is of independent interest. We then prove a general theorem which guarantees (with bounded denominator) when such Maass singular moduli are algebraic. As an example of these results, we derive a formula for the partition function p(n) as a finite sum of algebraic numbers which lie in the usual discriminant −24n + 1 ring class field. We indicate how these results extend to general weights. In particular, we illustrate how one can compute theta lifts for general weights by making use of the Kudla-Millson kernel and Maass differential operators.

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Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors

Abstract: Die Deutsche Bibliothek -CIP-Einheitsaufnahme Bruinier, Jan Hendrik: Borcherds products on 0(2,1) and Chern classes of Heegner divisors / Jan H.

Cited by 303 publications

References 0 publications

Hilbert Modular Forms and Their Applications

Hilbert Modular Forms and Their Applications

SO(3)–Donaldson invariants of ℂP²and mock theta functions

Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

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Borcherds Products on O(2, l) and Chern Classes of Heegner Divisors

Abstract: Die Deutsche Bibliothek -CIP-Einheitsaufnahme Bruinier, Jan Hendrik: Borcherds products on 0(2,1) and Chern classes of Heegner divisors / Jan H.

Cited by 303 publications

References 0 publications

Hilbert Modular Forms and Their Applications

Hilbert Modular Forms and Their Applications

SO(3)–Donaldson invariants of ℂP2and mock theta functions

Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms

Contact Info

Product

Resources

About

SO(3)–Donaldson invariants of ℂP²and mock theta functions