$p$-adic Mathematical Physics and V. S. Vladimirov Works

After a brief reminder of the basic principles of p-adic mathematical physics, we will discuss recent developments in the quantum zeta function. V.S. Vladimirov is one of the founders of p-adic mathematical physics. His works on spectral theory in p-adic quantum mechanics, fractional differential operator and non-linear pseudo-differential equations will be discussed in the context of recent developments.