Tunnel ionization belongs to the fundamental processes of atomic physics. The so-called two-step model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the time-dependent Sch...

Let k be a number field with ring of adeles A, let B be a quaternion algebra defined over k, and letG = B×. Let π be an infinite dimensional irreducible cuspidal automorphic representation of G(A). Then the vanishing or nonvanishing of L(1/2, π) has been conjectured or shown to be equivalent to conditions of considerable interest in number theory or automorphic representation theory. For exampl...

We study possibilities to realize a nonvanishing finite Wilson line (WL) scalar mass in flux compactification. Generalizing loop integrals the quantum correction WL at one-loop, we derive conditions for and mode sums one-loop corrections be finite. further guess classify four-point three-point interaction terms satisfying these conditions. As an illustration, is explicitly shown six dimensional...

In this article we prove that given a holomorphic cusp form f and any point s0 in the complex plane, there is a holomorphic cusp form g such that the Rankin-Selberg L-function L(s, f × g) is non-zero at s0. Résumé: Dans cet article, on prouve le résultat suivant. Etat donné une forme holomorphe cuspidale f et un point quelquonque du plan complexe, il existe une forme holomorphe cuspidale g tell...

Motivated by work of Gross, Rohrlich, and more recently Kim, Masri, and Yang, we investigate the nonvanishing of central values of L-functions of “canonical” weight 2k−1 Hecke characters for Q( √ −p), where 3 < p ≡ 3 (mod 4) is prime. Using the work of Rodriguez-Villegas and Zagier, we show that there are nonvanishing central values provided that p ≥ 6.5(k−1) and (−1) ( 2 p ) = 1. Moreover, we ...