In [4], Haran, using Riesz potentials, presents a version of the classical explicit formula for the Riemann zeta function that treats all places equally. In this article, we extend Haran's results to the case of an imaginary quadratic extension of …
The main goal of this article is to study a new class of nonlocal operators and the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated with them. The fundamental solutions of these equations are transition …
In this paper we deal with the operator defined as 𝑓(∂,𝛼)𝜙:=−1𝜉→𝑥(|𝑓(𝜉)|𝛼𝑝𝑥→𝜉𝜙), where f(ξ) is an elliptic quadratic form of dimension 3 over ℚ p . We study the Cauchy problem associated that operator, and find the fundamental solution and some …