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Let f be a normalized Hecke eigenform of weight k for the full modular group S L 2 (ℤ). In this paper, we obtain the asymptotic of higher moments of general divisor functions associated to the Fourier coefficients of Rankin–Selberg L-functions R (s , f × f) , supported at the integers represented by primitive integral positive-definite binary quadratic forms (reduced forms) of a fixed discriminant D < 0. We improve previous results in the case when the reduced form is given by (x 1 , x 2) = x 1 2 + x 2 2 . [ABSTRACT FROM AUTHOR]

We define four functions F 1 ∗ , F 2 ∗ , F 3 ∗ and F 4 ∗ as finite field analogues of Appell series F 1 , F 2 , F 3 and F 4 , respectively using purely Gauss sums in the spirit of finite field hypergeometric series introduced by McCarthy. We establish relations among F 1 ∗ , F 2 ∗ and F 3 ∗ analogous to those satisfied by the classical Appell series. Recently, several people have defined finite field analogues of Appell series using integral representations of Appell series. We show that our functions F 1 ∗ , F 2 ∗ and F 3 ∗ are closely related to those functions. [ABSTRACT FROM AUTHOR]

Cobalt oxide nanoparticles (size 2 to 3.5 nm) were successfully impregnated on an alumina-silica (mixed oxide) support through an experimentally viable and easily reproducible protocol. The prepared material was well characterized by XRD, HR-TEM, BET surface area, EDX and XPS analyses. Porous alumina-silica having a high surface area served as a protective heterogeneous support on which the well-dispersed Co3O4 nanoparticles served as an active catalytic species for the hydrazine-mediated transfer hydrogenation of nitroarenes. About 2 mol % of the active catalyst in ethanol at 60 °C was adequate for a successful conversion. Moreover, transfer hydrogenation of nitroarenes by the catalyst was found to take place chemoselectively in the presence of other labile functional groups such as halide, alkene, nitrile, carbonyl, and ester. This inexpensive catalyst was also able to catalyze the reaction on a gram scale reaction and found to be robust and recyclable up to eight runs. [ABSTRACT FROM AUTHOR]

Cobalt oxide nanoparticles (size 2 to 3.5 nm) were successfully impregnated on an alumina-silica (mixed oxide) support through an experimentally viable and easily reproducible protocol. The prepared material was well characterized by XRD, HR-TEM, BET surface area, EDX and XPS analyses. Porous alumina-silica having a high surface area served as a protective heterogeneous support on which the well-dispersed Co 3 O 4 nanoparticles served as an active catalytic species for the hydrazine-mediated transfer hydrogenation of nitroarenes. About 2 mol % of the active catalyst in ethanol at 60 °C was adequate for a successful conversion. Moreover, transfer hydrogenation of nitroarenes by the catalyst was found to take place chemoselectively in the presence of other labile functional groups such as halide, alkene, nitrile, carbonyl, and ester. This inexpensive catalyst was also able to catalyze the reaction on a gram scale reaction and found to be robust and recyclable up to eight runs., (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)