All Questions
Tagged with sp.spectral-theory nt.number-theory
9 questions with no upvoted or accepted answers
12
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Weyl law for Maass forms with nontrivial character
The classical Weyl law for $\Gamma = \mathrm{SL}_2(\mathbb{Z})$ counts the number of Maass cusp forms on $\Gamma \backslash \mathbb{H}$ with Laplace eigenvalue less than $T$. This is originally due to ...
- 8,374
7
votes
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291
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"Non-critical" zeros of $\zeta$ and the $\zeta$-cycles of Connes and Consani
In the recent preprint of Connes and Consani https://arxiv.org/abs/2106.01715 a new spectral realization of the critical zeros of $\zeta$ (edit: defined as being those on the critical line only, see ...
- 883
6
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348
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Recent work on Pseudo-Laplacian and Pseudo-cuspform in the spirit of Riemann Hypothesis after the work of Bombieri and Garrett
( This is my first MO question . I'm totally inexperienced on MO so, forgive me for my mistakes .)
Paul Garrett and Enrico Bombieri were (are?) Secretly Working on Pseudo-Laplacians and Pseudo-...
user153636
5
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0
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262
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p-adic analogue of self-adjoint operator
Consider the very well-known result that any Hermitian matrix over $\mathbb{C}$, say $T$, admits a decomposition $T = UDU^*$ where $U$ is unitary and $D$ is diagonal with real entries. I am looking ...
5
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539
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An inverse eigenvalue problem on Jacobi matrices
I am interested in trying to design a Hermitian Jacobi (tridiagonal) matrix $H$ that has specific properties. The basic property, which is simple enough to construct, is that for an $N\times N$ matrix ...
- 291
4
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624
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The Bilu-Linial conjecture and Ramanujan graphs
The Bilu-Linial conjecture claims that every $d-$regular graph has a $2-$lift such that for the signing matrix has its eigenvalues between $[-2\sqrt{d-1},2\sqrt{d-1}]$ (the ``signing matrix" is the ...
- 1,893
3
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186
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Bourgain-Gamburd-like theorems in the non-algebraic case
For $\mu$ a Borel probability measure on the compact group $G=\operatorname{SU}(d)$, Bourgain-Gamburd prove that the spectral radius of the associated operator on $L^2(G)$ is strictly less than one, ...
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2
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110
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Spectral decomposition of idele class group $L^2(\mathbb{I}_F/ F^{\times})$
Let $F$ be a number field. Let $\mathbb{A}_F$ be the ring of adeles. The group of units of $\mathbb{A}_F$ is called the group of ideles $\mathbb{I}_F=\mathbb{A}_F^{\times}= GL_1(\mathbb{A}_F)$. The ...
- 421
1
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0
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239
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Norm related to diophantine approximation?
I'm trying to read this paper: Bourgain, J.; Jitomirskaya, S., Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential, J. Stat. Phys. 108, No. 5-6, 1203-1218 (2002), ...
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