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A classification of harmonic weak Maaß forms of half-integral weight
We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maaß forms with exponential growth allowed at...
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Relating Siegel cusp forms to Siegel–Maaß forms
In this paper we generalize a well-known isomorphism between the space of cusp forms of weight k for a Fuchsian subgroup of the first kind
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Locally harmonic Maass forms of positive even weight
We twist Zagier’s function f k,D by a sign function and a genus character. Assuming weight 0 < k ≡ 2 (mod 4), and letting D be a positive non-square...
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On the Random Wave Conjecture for Dihedral Maaß Forms
We prove two results on arithmetic quantum chaos for dihedral Maaß forms, both of which are manifestations of Berry’s random wave conjecture: Planck...
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A Note on Mock Automorphic Forms and the BPS Index
AbstractWe discuss mock automorphic forms from the point of view of representation theory, that is, mock automorphic forms obtained from weak...
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On Kleinian mock modular forms
We give an explicit and computationally efficient construction of harmonic weak Maass forms which map to weight 2 newforms under the
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The first moment of Maaß form symmetric square L-functions
We prove an asymptotic formula for the twisted first moment of Maaß form symmetric square L -functions on the critical line and at the central point....
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On Weierstrass mock modular forms and a dimension formula for certain vertex operator algebras
Using techniques from the theory of mock modular forms and harmonic Maaß forms, especially Weierstrass mock modular forms, we establish several...
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The twelfth moment of Hecke L-functions in the weight aspect
We prove an upper bound for the twelfth moment of Hecke L -functions associated to holomorphic Hecke cusp forms of weight k in a dyadic interval
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A symplectic restriction problem
We investigate the norm of a degree 2 Siegel modular form of asymptotically large weight whose argument is restricted to the 3-dimensional subspace...
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Analytic Properties of Spherical Cusp Forms on GL(n)
Let φ be an L 2 -normalized spherical vector in an everywhere unramified cuspidal automorphic representation of PGL n over ℚ with Laplace eigenvalue λ φ ....
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The unipotent mixing conjecture
We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves.
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The modularity of Siegel’s zeta functions
Siegel defined zeta functions associated with indefinite quadratic forms, and proved their analytic properties such as analytic continuations and...
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Generalizations
We conclude with the consideration of modular forms of half-integral weight and some real-analytic generalizations of modular forms. In particular,...
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On the global sup-norm of GL(3) cusp forms
Let φ be a spherical Hecke–Maaß cusp form on the non-compact space PGL 3 (ℤ)PGL 3 (ℝ). We establish various pointwise upper bounds for φ in terms of its...
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The Hilbert modular group and orthogonal groups
We derive an explicit isomorphism between the Hilbert modular group and certain congruence subgroups on the one hand and particular subgroups of the...