For a quasi-split classical group over p-adic field with sufficiently large residual characteristic, we prove that the maximum depth of representation in each L-packet equals corresponding L-parameter. Furthermore, for unitary groups, show is constant L-packet. The key an analysis endoscopic character relation via harmonic based on Bruhat–Tits theory. These results are slight generalizations re...

In this paper, we study special cycles on the Krämer model of $$\mathrm {U}(1,1)(F/F_0)$$ -Rapoport–Zink spaces where $$F/F_0$$ is a ramified quadratic extension p-adic number fields with assumption that 2-dimensional hermitian space quasi-homomorphisms anisotropic. We write down decomposition these and prove version Kudla–Rapoport conjecture in case. then apply local results to compute interse...

We introduce the notion of a p-adic quantum bit ( p-qubit) in context mechanics initiated and developed after seminal paper Volovich [Theor. Math. Phys. 71, 574 (1987)]. In this approach, physics takes place three-dimensional space rather than Euclidean space. Based on our prior work describing special orthogonal group [Di Martino et al., arXiv:2104.06228 [math.NT] (2021)], we outline program t...

Let p be prime, N be a positive integer prime to p, and k be an integer. Let Pk(t) be the characteristic series for Atkin’s U operator as an endomorphism of p-adic overconvergent modular forms of tame level N and weight k. Motivated by conjectures of Gouvêa and Mazur, we strengthen a congruence in [W] between coefficients of Pk and Pk′ for k ′ p-adically close to k. For p − 1 | 12, N = 1, k = 0...