Non-vanishing of LL-functions associated to cusp forms of half-integral weight

In this article, we prove non-vanishing results for $L$-functions associated to holomorphic cusp forms of half-integral weight on average (over an orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings (Springer

The Saito-Kurokawa lifting and Darmon points

Let E_{/_\Q} be an elliptic curve of conductor $Np$ with $p\nmid N$ and let $f$ be its associated newform of weight 2. Denote by $f_\infty$ the $p$-adic Hida family passing though $f$, and by $F_\infty$ its $\Lambda$-adic Saito-Kurokawa lift. The $p$-adic family $F_\infty$ of Siegel modular forms admits a formal Fourier expansion, from which we can define a family of normalized Fourier coefficients $\{\widetilde A_T(k)\}_T$ indexed by positive definite symmetric half-integral matrices $T$ of size $2\times 2$. We relate explicitly certain global points on $E$ (coming from the theory of Stark-Heegner points) with the values of these Fourier coefficients and of their $p$-adic derivatives, evaluated at weight $k=2$.Comment: 14 pages. Title change

On the special values of certain L-series related to half-integral weight modular forms

Let h be a cuspidal Hecke eigenform of half-integral weight, and En/2+1/2 be Cohen’s Eisenstein series of weight n/2+1/2. For a Dirichlet character χ we define a certain linear combination R(χ)(s, h,En/+1/2) of the Rankin-Selberg convolution products of h and En/2+1/2 twisted by Dirichlet characters related with χ. We then prove a certain algebraicity result for R(χ)(l, h,En/2+1/2) with l integers

Combinatorial sputter synthesis of single-phase La(XYZ)O3±σ_{3\pm\sigma} perovskite thin film libraries: a new platform for materials discovery

Compositionally complex perovskites provide the opportunity to develop stable and active catalysts for electrochemical applications. The challenge lies in the identification of single-phase perovskites with optimized composition for high electrical conductivity. Leveraging a recently discovered effect of self-organized thin film growth during reactive sputtering, La-Co-Mn-O and La-Co-Mn-Fe-O perovskite (ABO3) thin film materials libraries are synthesized. These show phase-pure La-perovskites over a wide range of chemical composition variation for the B-site elements for deposition temperatures equal to or higher than 300$^\circ$C. It is demonstrated that this approach enables the discovery and tailoring of chemical compositions for desired optical bandgap and electrical conductivity, and thereby opens the path for the targeted development of e.g. new high-performance electrocatalysts

Изучение гидролитической устойчивости и растворимости стампирина

Представлены результаты исследования гидролитической устойчивости стампирина I (1-фенил-2,3-диметил-4-стеароиламино-5-пиразолона)-нового противовоспалительного средства в различных средах и условиях и его растворимости в некоторых органических растворителях. Показано, что наиболее подходящими условиями полного гидролиза I является кипячение его на воздушной бане в 25% растворе соляной кислоты в течение 45 минут. В водной и щелочной средах I является гидролитически устойчивым. Определена растворимость I в граммах на 100 мл раствора при 20° С весовым методом. Она равна 1,31 в этиловом спирте, 1,01 в изопропиловом спирте, 0,07 в диэтиловом эфире, 3,77 в бензоле, 0,79 в четыреххлористом углероде. В воде I практически не растворим

Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables

Let $-d$ be a a negative discriminant and let $T$ vary over a set of representatives of the integral equivalence classes of integral binary quadratic forms of discriminant $-d$. We prove an asymptotic formula for $d \to \infty$ for the average over $T$ of the number of representations of $T$ by an integral positive definite quaternary quadratic form and obtain results on averages of Fourier coefficients of linear combinations of Siegel theta series. We also find an asymptotic bound from below on the number of binary forms of fixed discriminant $-d$ which are represented by a given quaternary form. In particular, we can show that for growing $d$ a positive proportion of the binary quadratic forms of discriminant $-d$ is represented by the given quaternary quadratic form.Comment: v5: Some typos correcte