Author

Aryaman Chandra

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Preprint Aug 2026

On The Spectral Properties of Discrete Landscape Functions

We study the landscape function on a discretized interval. The discrete landscape has an explicit closed form, and its spectral coefficients can be computed exactly. We show that these coefficients lie in explicit abelian extensions of $\mathbb{Q}$, and obtain the bound $[\mathbb{Q}(c_k(N)):\mathbb{Q}]\leq\varphi(N)$ f...

Aryaman Chandra, S. Jain · 0 citations

Preprint Jul 2026

Arithmetic Landscape Functions of a Discrete Cat Map

We study the diagonal Green function $\widetilde{u}(x)=[L_N^{-1}]_{x,x}$ of the operator $L_N=I-\alpha P$ on the finite torus $(\mathbb{Z}/N\mathbb{Z})^2$, where $P$ is the transfer operator of the discrete cat map $T_N(x)=Ax \bmod N$. We prove the exact formula $\widetilde{u}(x)=(1-\alpha^{k_x})^{-1}$, where $k_x$ is...

Aryaman Chandra · 1 citation