A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Reading tea leaves worldwide: decoupled drivers of initial litter decomposition mass-loss rate and stabilisation

The breakdown of plant material fuels soil functioning and biodiversity. Currently, process understanding of global decomposition patterns and the drivers of such patterns are hampered by the lack of coherent large-scale datasets. We buried 36,000 individual litterbags (tea bags) worldwide and found an overall negative correlation between initial mass-loss rates and stabilization factors of plant-derived carbon, using the Tea Bag Index (TBI). The stabilization factor quantifies the degree to which easy-to-degrade components accumulate during early-stage decomposition (e.g. by environmental limitations). However, agriculture and an interaction between moisture and temperature led to a decoupling between initial mass-loss rates and stabilization, notably in colder locations. Using TBI improved mass-loss estimates of natural litter compared to models that ignored stabilization. Ignoring the transformation of dead plant material to more recalcitrant substances during early-stage decomposition, and the environmental control of this transformation, could overestimate carbon losses during early decomposition in carbon cycle models

COMPENDIUM OF EXPERIMENTAL RESULTS OF THE CIRCULATION OF AQUEOUS THORIUM OXIDE SLURRIES IN TOROIDS

Data are presented for all toroid runs which circulated aqueous thorium oxide slurries between August 1954, and October 1956. In addition, a tabulation of the properties of numerous thoria preparatiors is presented. (auth