Janyarak Tongsomporn

This work investigates the solution and the stability of a generalized system of bi-quadratic–Drygas functional equations in non-Archimedean normed spaces with unknown coefficients. The presence of asymmetric coefficients and reflection terms induces nontrivial coupling effects and symmetry-breaking phenomena, while simultaneously capturing additive, quadratic, and mixed additive–quadratic behaviors. An examination of the coefficients shows that the trivial solution is the only one satisfying the system of equations in asymmetric parameter configurations. For symmetric configurations, by exploiting the ultrametric structure of non-Archimedean norms and applying an iterative method combined with symmetry-based decomposition into even and odd parts, we establish the existence and uniqueness of an exact solution approximating a given mapping. Several known stability results for bi-Drygas functional equations are recovered with improvement as special cases.

This paper investigates the Hyers–Ulam stability of a class of generalized biquadratic functional equations involving four unknown mappings in non‐Archimedean normed spaces. We analyze a coupled system that simultaneously incorporates additive, quadratic, additive–quadratic, and quadratic–additive behaviors, thereby capturing both symmetric and asymmetric interactions among the variables. By exploiting the ultrametric structure inherent in non‐Archimedean normed spaces, we establish the existence and uniqueness of approximating solutions, together with stability bounds. Furthermore, a known stability result for biquadratic functional equations is recovered as a corollary of the main theorem.

We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t^13/84+ϵ as t → ∞. For both, the Riemann zeta function as well as for the more general Lerch zeta function, it is conjectured that the right-hand side can be replaced by t^ϵ (which is the so-called Lindelöf hypothesis). The growth of an analytic function is closely related to the distribution of its zeros.

We introduce a generalized adjacency matrix in order to distinguish cospectral graphs. Our reasoning is motivated by the work of Johnson and Newman and properties of p-adic numbers. Using a polynomial time algorithm, we comment on computer experiments with which we can distinguish cospectral (non-isomorphic) graphs.