Tootfinder

On the equational theory of finite modular lattices
Christian Herrmann
https://arxiv.org/abs/2406.04237 https://arxiv.org/pdf/2406.04…

On the equational theory of finite modular lattices
It is shown that the equational theory of modular lattices is undecidable

Cycle integrals of meromorphic Hilbert modular forms
Claudia Alfes, Baptiste Depouilly, Paul Kiefer, Markus Schwagenscheidt
https://arxiv.org/abs/2406.03465

Cycle integrals of meromorphic Hilbert modular forms
We establish a rationality result for linear combinations of traces of cycle integrals of certain meromorphic Hilbert modular forms. These are meromorphic counterparts to the Hilbert cusp forms $ω_m(z_1,z_2)$, which Zagier investigated in the context of the Doi-Naganuma lift. We give an explicit formula for these cycle integrals, expressed in terms of the Fourier coefficients of harmonic Maass forms. A key element in our proof is the explicit construction of locally harmonic Hilbert-Maass form…

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This https://arxiv.org/abs/2405.17021 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Truncated Modular Exponentiation Operators: A Strategy for Quantum Factoring
Modular exponentiation (ME) operators are one of the fundamental components of Shor's algorithm, and the place where most of the quantum resources are deployed. I propose a method for constructing the ME operators that relies upon the simple observation that the work register starts in state $\vert 1 \rangle$. Therefore, we do not have to create an ME operator $U$ that accepts a general input, but rather, one that takes an input from the periodic sequence of states $\vert f(x) \rangle$ for $x \…

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On a parity result for the symmetric square of modular forms with congruent residual representations
Jishnu Ray
https://arxiv.org/abs/2406.03050 https://…

On a parity result for the symmetric square of modular forms with congruent residual representations
The parity of Selmer ranks for elliptic curves defined over the rational numbers $\mathbb{Q}$ with good ordinary reduction at an odd prime $p$ has been studied by Shekhar. The proof of Shekhar relies on proving a parity result for the $λ$-invariants of Selmer groups over the cyclotomic $\mathbb{Z}_p$-extension $\mathbb{Q}_\infty$ of $\mathbb{Q}$. This has been further generalized for elliptic curves with supersingular reduction at $p$ by Hatley and for modular forms by Hatley--Lei. In this p…

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Medialer Strassenrealismus I #Fotografie, Bildbeschreibung: Ein Mann in Lederjacke auf einer Bank der Tramhalte, eine Bierdose, hinter ihm ein junges Mädchen in Jacke mit Pelzkragen, Hinterkopf, schaut "aus dem Bild heraus".

This https://arxiv.org/abs/2307.14131 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On $r$-isogenies over $\mathbb{Q}(ζ_r)$ of elliptic curves with rational $j$-invariants
The main goal of this paper is to determine for which prime numbers $r\geq 3$ can an elliptic curve~$E$ defined over $\mathbb Q$ have an $r$-isogeny over $\mathbb Q(ζ_r)$. We study this question under various assumptions on the 2-torsion of $E$. Apart from being a natural question itself, the mod~$r$ representations attached to such $E$ arise in the Darmon program for the generalized Fermat equation of signature $(r,r,p)$, playing a key role in the proof of modularity of certain Frey varieties…