The Growth of Cosmological Perturbations in the Transition Eras

In this article we determine the dominating modes of the cosmological perturbations in different transition eras of the universe evolution (namely, radiation-dust, dust-vacuum, dust-K-matter, and K-matter-vacuum) in a covariant and gauge-invariant manner.     

On the Signs of Fourier Coefficients of Cusp Forms

Let be a discrete subgroup of SL(2, ) with a fundamental region of finite hyperbolic volume. (Then, is a finitely generated Fuchsian group of the first kind.) Let 0}} {a(n)e^{2\pi i(n + {\kappa })z/{\lambda }} } ,{ }z \in \mathcal{H}.$$ " align="middle" border="0"> be a nontrivial cusp form, with multiplier system, with respect to . Responding to a question of Geoffrey Mason, the authors present simple proofs of the following two results, under natural restrictions upon . Theorem. If the coefficients a(n) are real for all n, then the sequence {a(n)} has infinitely many changes of sign. Theorem. Either the sequence {Re a(n)} has infinitely many sign changes or Re a(n) = 0 for all n. The same holds for the sequence {Im a(n)}.     

Orthogonality and Hecke operators

In this article we analyze orthogonality relations between old forms and the connection to the theory of Hecke operators.     

Über eine Verallgemeinerung des Problems von Chowla und Walum

Ohne Zusammenfassung     

Empirical processes indexed by smooth functions

In this paper we derive a general invariance principle for empirical processes indexed by smooth functions. The method is applied to prove bounds for the convergence of the empirical distributions which might be useful to verify asymptotic normality of smooth statistical functionals. As one further application we get the convergence of the so-called empirical characteristic function process.     

Holomorphe Systeme von Pseudodifferentialoperatoren

Ohne Zusammenfassung