Tootfinder

On $p$-th cyclotomic field and cyclotomic matrices involving Jacobi sums
Hai-Liang Wu, Li-Yuan Wang, Hao Pan
https://arxiv.org/abs/2506.14316 https://

On $p$-th cyclotomic field and cyclotomic matrices involving Jacobi sums
As a complement to our previous article, in this paper we determine the explicit values of $\det\left[J_p(χ^{ki},χ^{kj})\right]_{1\le i,j\le n-1}$ and $\det \left[J_p(χ^{ki},χ^{kj})\right]_{0\le i,j\le n-1}$, where $p$ is a prime, $1\le k

Einstein causality of quantum measurements in the Tomonaga-Schwinger picture
Samuel Fedida
https://arxiv.org/abs/2506.14693 https://a…

Einstein causality of quantum measurements in the Tomonaga-Schwinger picture
When quantum measurements are conducted over spacelike-separated regions of spacetime, a natural and commonly assumed physical postulate, called Einstein causality, asserts that they should commute. In this paper, we provide a generalisation to Lüders' rule à la Aharonov-Albert in those globally hyperbolic spacetimes which allow unitarily equivalent Hilbert spaces to be defined along Cauchy hypersurfaces, thus relying on the existence of an interaction picture à la Tomonaga-Schwinger. We sho…

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Causality in the human niche: lessons for machine learning
Richard D. Lange, Konrad P. Kording
https://arxiv.org/abs/2506.13803 https://

Causality in the human niche: lessons for machine learning
Humans interpret the world around them in terms of cause and effect and communicate their understanding of the world to each other in causal terms. These causal aspects of human cognition are thought to underlie humans' ability to generalize and learn efficiently in new domains, an area where current machine learning systems are weak. Building human-like causal competency into machine learning systems may facilitate the construction of effective and interpretable AI. Indeed, the machine learnin…

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Intersections of blocks of cyclotomic Hecke algebras
Maria Chlouveraki, Gunter Malle
https://arxiv.org/abs/2506.12973 https://arxiv.o…

Intersections of blocks of cyclotomic Hecke algebras
Trinh and Xue have proposed a startling conjecture on intersections of blocks of cyclotomic Hecke algebras occurring in modular representation theory of finite reductive groups. We prove this conjecture for all exceptional type groups apart from $E_8$. We also propose several generalisations, to Suzuki and Ree groups, to non-rational Coxeter groups and even more generally to spetsial complex reflection groups, and confirm these in various cases.

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Complex forming behaviour of {\alpha}, \b{eta} and {\gamma}-cyclodextrins with varying size probe particles in silico
N. R. M. Nelumdeniya, R. J. K. U. Ranatunga
https://arxiv.org/abs/2506.13115

Complex forming behaviour of α, \b{eta} and γ-cyclodextrins with varying size probe particles in silico
Cyclodextrins (CDs) are cyclic oligosaccharides composed of glucopyranose units bonded together to form a truncated cone that can make inclusion complexes with guest molecules. The α, \b{eta}, and γ-CDs, which respectively comprise six, seven or eight glucopyranose units, are used extensively in pharmaceutical formulations as functional excipients. The cavity sizes of all three natural CDs have been approximated using static structures but a growing consensus is that the CDs are flexible; mor…

Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field
Zhonghua Li, Yutong Song, Qiyu Yang, Shengbo Zhao
https://arxiv.org/abs/2506.12342

Extreme values of derivatives of the Dedekind zeta function of a cyclotomic field
In this paper, we establish a lower bound for the maximum of derivatives of the Dedekind zeta function of a cyclotomic field on the critical line. Employing a double version convolution formula and combing special GCD sums, our result generalizes the work of Bondarenko et al. and Fonga in 2023. We also set a lower bound by the resonance method when the real part is near the critical line, both of the above results refine part of Yang's work in 2022.

A note on instantaneous gelation for coagulation kernels vanishing on the diagonal
Iulia Cristian (LJLL), Barbara Niethammer, Juan J. L. Vel\'azquez
https://arxiv.org/abs/2506.11573

A note on instantaneous gelation for coagulation kernels vanishing on the diagonal
We prove that instantaneous gelation (i.e., instantaneous loss of mass) occurs for coagulation equations with sum-type kernels of homogeneity greater than one which vanish on the diagonal. Our proof includes solutions that are Radon measures if we exclude the case of initial data that are a single Dirac delta.