Results 31 to 40 of about 230 (160)

On the Lang–Trotter conjecture for Siegel modular forms

Mathematika, Volume 72, Issue 3, July 2026.
Abstract Let f$f$ be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with f$f$, generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues ap$a_p$ of f$f$, and obtain upper
Arvind Kumar, Moni Kumari, Ariel Weiss
wiley   +1 more source

Squashed toric manifolds and higher depth mock modular forms

Journal of High Energy Physics, 2019
Squashed toric sigma models are a class of sigma models whose target space is a toric manifold in which the torus fibration is squashed away from the fixed points so as to produce a neck-like region.
Rajesh Kumar Gupta, Sameer Murthy, Caner Nazaroglu   +2 more
doaj   +1 more source

Primitivity testing in free group algebras via duality

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract Let K$K$ be a field and F$F$ a free group. By a classical result of Cohn and Lewin, the free group algebra KF$K\left[F\right]$ is a free ideal ring (FIR): a ring over which the submodules of free modules are themselves free, and of a well‐defined rank. Given a finitely generated right ideal I⩽KF$I\leqslant K\left[F\right]$ and an element f∈I$f\
Matan Seidel, Danielle Ernst‐West, Doron Puder   +2 more
wiley   +1 more source

From living to fossil: ancestral state reconstruction of leaf architecture in extant Lauraceae and its relevance for the fossil record

Palaeontology, Volume 69, Issue 3, 2026.
Abstract Lauraceae are a tropical–subtropical angiosperm family that exhibit significant diversity and a rich fossil record, primarily of leaves found worldwide from the Cretaceous to the present. However, the taxonomic placement of many fossil leaves remains uncertain because of morphological convergence and limited variation in leaf characters among ...
Marco A. Rubalcava‐Knoth, Angélica Quintanar‐Castillo, Ana L. Hernández‐Damián, Sergio R. S. Cevallos‐Ferriz   +3 more
wiley   +1 more source

Algebraicity of ratios of special L$L$‐values for GL(n)$\mathrm{GL}(n)$

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We prove, under certain assumptions, the algebraicity of the ratio L(m,Π×χ)/L(m,Π×χ′)$L(m, \Pi \times \chi)/L(m, \Pi \times \chi ^{\prime })$, where Π$\Pi$ is a cuspidal automorphic cohomological unitary representation of GLn(AQ)$\mathrm{GL}_n(\mathbb {A}_\mathbb {Q})$, and χ$\chi$, χ′$\chi ^{\prime }$ are finite‐order Hecke characters such ...
Ankit Rai, Gunja Sachdeva
wiley   +1 more source

The Dimension of Spaces of Automorphic Forms [PDF]

American Journal of Mathematics, 1963
1. The trace formula of Selberg reduces the problem of calculating the dimension of a space of automorphic forms, at least when there is a compact fundamental domain, to the evaluation of certain integrals. Some of these integrals have been evaluated by Selberg.
openaire   +1 more source

Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the String‐Theoretical Swampland Programme

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
wiley   +1 more source

Tessellation Groups, Harmonic Analysis on Non‐Compact Symmetric Spaces and the Heat Kernel in View of Cartan Convolutional Neural networks

Fortschritte der Physik, Volume 74, Issue 4, April 2026.
ABSTRACT In this paper, we continue the development of the Cartan neural networks programme, launched with three previous publications, by focusing on some mathematical foundational aspects that we deem necessary for our next steps forward. The mathematical and conceptual results are diverse and span various mathematical fields, but the inspiring ...
Pietro Fré, Federico Milanesio, Marcelo Oyarzo, Matteo Santoro, Mario Trigiante   +4 more
wiley   +1 more source

Failure of stability of a maximal operator bound for perturbed Nevo–Thangavelu means

Mathematika, Volume 72, Issue 2, April 2026.
Abstract Let G$G$ be a two‐step nilpotent Lie group, identified via the exponential map with the Lie‐algebra g=g1⊕g2$\mathfrak {g}=\mathfrak {g}_1\oplus \mathfrak {g}_2$, where [g,g]⊂g2$[\mathfrak {g},\mathfrak {g}]\subset \mathfrak {g}_2$. We consider maximal functions associated to spheres in a d$d$‐dimensional linear subspace H$H$, dilated by the ...
Jaehyeon Ryu, Andreas Seeger
wiley   +1 more source