Some Congruences Modulo Primes

 We shall prove a sequence of congruences modulo odd primes p which can be viewed as generalizations of a congruence first proved by Zhi-Wei Sun in 1995. Received 2 December 1997     

On Riesz means of the coefficients of spinor zeta functions in genus two

Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp ₂(?) of genus 2. The Fourier coefficients of the spinor zeta function Z _F (s) are denoted by c _n . Let D _ρ (x;Z _F ) be the Riesz mean of c _n . In this paper, we obtain the truncated Voronoï-type formula of D _ρ (x;Z _F ) under the Ramanujan–Petersson conjecture.     

Pointwise multipliers for Besov spaces of dominating mixed smoothness-Ⅱ

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R~d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R~d).     

Transcendence of zeros of Jacobi forms

A special case of a fundamental theorem of Schneider asserts that if \(j(\tau )\) is algebraic (where j is the classical modular invariant), then any zero z not in \(\mathbf{Q}.L_\tau := \mathbf{Q}\oplus \mathbf{Q}\tau \) of the Weierstrass function \(\wp (\tau ,\cdot )\) attached to the lattice \(L_\tau =\mathbf{Z}\oplus \mathbf{Z}\tau \) is transcendental. In this note we generalize this result to holomorphic Jacobi forms of weight k and index \(m\in \mathbf{N}\) with algebraic Fourier coefficients.     

On the Interplay of Regularity and Decay in Case of Radial Functions II. Homogeneous Spaces

We deal with decay and boundedness properties of elements of radial subspaces of homogeneous Besov and Triebel-Lizorkin spaces. For the region of parameters which are of interest for us these homogeneous spaces are larger than the inhomogeneous counterparts. By switching from the inhomogeneous spaces to the homogeneous classes the properties of the radial elements change. Our investigations are based on the atomic decompositions for radial subspaces in the sense of Epperson and Frazier (J.?Fourier Anal Appl. 1:311?C353, 1995). Finally, we apply these results for deriving some assertions on compact embeddings on unbounded domains.     

Study of hydrogenated AlN as an anti‐reflective coating and for the effective surface passivation of silicon

Stacks of aluminum oxide and silicon nitride are frequently used in silicon photovoltaics. In this Letter, we demonstrate that hydrogenated aluminum nitride can be an alternative to this dual‐layer stack. Deposited on 1 Ω cm p‐type FZ silicon, very low effective surface recombination velocities of 8 cm/s could be reached after firing at 820 °C. This excellent passivation is traced back to a high density of fixed charges at the interface of approximately –1 × 10¹² cm^–2 and a very low interface defect density below 5 × 10¹⁰ eV^–1 cm^–2. Furthermore, spectral ellipsometry measurements reveal that these aluminum nitride layers have ideal optical properties for use as anti‐reflective coatings. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)