We consider the critical values of symmetric power L-functions attached to elliptic curves over Q. We show how to calculate a canonical Deligne period, and in several numerical examples, especially for sixth and tenth powers, we examine the factorisation of the rational number apparently obtained when one divides the critical value by the canonical period. This seems to provide some support for...

Abstract Let $f$ f be a cuspidal Hecke eigenform without complex multiplication. We prove the automorphy of symmetric power lifting $\operatorname{Sym}^{n} f$ Sym n for every $n \geq 1$ ≥ 1 .

Given a directed simple graph G = (V,E) and a cost function c : E → R+, the power of a vertex u in a directed spanning subgraph H is given by pH(u) = maxuv∈E(H) c(uv), and corresponds to the energy consumption required for the wireless node u to transmit to all nodes v with uv ∈ E(H). The power of H is given by p(H) = ∑ u∈V pH(u). Power Assignment seeks to minimize p(H) while H satisfies some c...

We discuss the dependence of the Shannon entropy of rank-1 normalized finite POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension two (for qubits). In this case we prove that the entropy is ...

We study the behaviour of a symmetric exclusion process in presence non-Markovian stochastic resetting, where configuration system is reset to step-like profile at power-law waiting times with an exponent $\alpha$. find that resetting leads rich for currents, as well density profile. show that, any finite system, $\alpha<1$, eventually becomes uniform while $\alpha >1$, eventual non-trivial sta...