Inspired by Borcherds' questions [2, 17.10], Guerzhoy constructed a new type of Hecke operators T(p), called the multiplicative Hecke operators, which acts on the space of meromorphic modular forms on the full modular group SL2(Z). In [17], this result was extended in two directions: to higher levels and to T(n) with a positive integer n. In this paper, building on the results in [17], we further generalize the result in another direction by considering alternative infinite product expansions of meromorphic modular forms. As an application, we demonstrate how multiplicative Hecke operators relate both the divisor of modular forms and traces of singular moduli. Additionally, we prove the existence of a modular form with nonintegral coefficients whose poles or zeros are only supported at the cusps and which is not a multiplicative Hecke eigenform. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
In this paper we study of a coupled thermoelastic system with viscoelastic damping term and Wentzell boundary conditions. We prove the existence as well as the stability of the energy associated to the problem. To prove the existence of solution we use semigroup theory and the stability is proved by multipliers techniques. The main goal is to bring the viscoelastic damping into the discussion concerning thermoelastic systems with Wentzell boundary conditions.
This paper investigates the solvability, stability, and convergence of numerical solutions for nonlinear stochastic differential-algebraic equations (SDAEs) with time-varying coefficients. We establish sufficient conditions for solvability and stochastic asymptotic stability, and prove that the explicit Euler method converges as the mesh size tends to zero. Moreover, we show that the solvability conditions are also necessary in the linear case. Several examples are presented to illustrate the theoretical results. To the best of our knowledge, these results are new for time-varying SDAEs.
Let B be the backward shift on ω=CN0, endowed with the product topology. We prove that there is a dense Gδ set of hypercyclic vectors x for which every infinite suborbit has dense linear span. This gives a negative answer to the locally convex version of a question of Faghih-Ahmadi and Hedayatian about supercyclic vectors. The same vectors can be chosen so that every proper closed affine subspace contains only finitely many points of the orbit. For each such x, every nonzero continuous linear operator A on ω, and every y∈ω, the equation ABnx=y has only finitely many solutions n∈N0. Moreover, two continuous linear operators that agree on an infinite suborbit are equal.
