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0answers
82 views

Asymptotic expansion of an integral, related to Maass forms

I am trying to compute the asymptotic expansion of the integral $I(t) = \int_{C} e^{\sqrt{1+u}(\frac{1}{t}+\frac{t^2}{\sqrt{u}})}\frac{u^\eta}{\sqrt{1+u}}du$ as $t$ is real and $t\rightarrow +\infty$, ...
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0answers
81 views

A database on Maass forms?

Is there somewhere a database on Maass forms? I mean something like a file with eigenvalues, coefficients etc. (I am interested in classical forms on $\Gamma(1)\backslash H$).
3
votes
3answers
564 views

Mock Theta Functions

I am studying about Mock modular forms and Mock theta functions. I wonder how Zwegers connected mock theta functions with Harmonic Maass Forms? I mean, what was the philosophy/idea of Mock Theta ...
4
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2answers
179 views

No Exceptional Eigenvalues of Weight 1/2 Maass Forms on $\Gamma_0(4)$?

Some colleagues and I were wondering if there is a citation out there which shows there are no exceptional eigenvalues, $\lambda$, of classical weight 1/2 Maass forms on $\Gamma_0(4)$, which is to say ...
3
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1answer
268 views

Weyl law for SL(2,C)

Are there any estimates for the eigenvalues of the Laplace operator for $\Gamma \backslash SL(2, \mathbb{C})/SU(2)$ known beyond the main term? Here, $\Gamma$ should be congruence subgroup in ...
5
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1answer
350 views

Are coefficients of Maass forms of eigenvalue 1/4 known to be algebraic?

I would really like to know whether the following famous conjecture has been solved. I've read in a few places that it has been solved, but I have been unable to find a reference. I do know that ...
4
votes
3answers
347 views

Equidistibution of horocycles through Hecke eigenvalues of Maass cusp forms

At the end of this very nice post: http://blogs.ethz.ch/kowalski/2012/05/21/who-needled-buffon/ E. Kowalski talks about the equidistribution of the points $\frac{j+i}{N}$ when $j=1,\dots,N$ and $N$ ...
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3answers
1k views

Are there Maass forms where the expected Galois representation is $\ell$-adic?

Recall that by theorems of Deligne and Deligne--Serre, there is the following dichotomy: Modular forms on the upper half plane of level $N$ and weight $k\geq 2$ correspond to representations ...