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Abstract Let$$P_1, \ldots , P_m \in \mathbb {K}[\mathrm {y}]$$be polynomials with distinct degrees, no constant terms and coefficients in a general local field$$\mathbb {K}$$. We give a quantitative count of the number of polynomial progressions$$x, x+P_1(y), \ldots , x + P_m(y)$$lying in a set$$S\subseteq \mathbb {K}$$of positive density. The proof relies on a general$$L^{\infty }$$inverse theorem which is of independent interest. This inverse theorem implies a Sobolev improving estimate for multilinear polynomial averaging operators which in turn implies our quantitative estimate for polynomial progressions. This general Sobolev inequality has the potential to be applied in a number of problems in real, complex andp-adic analysis. 

Abstract We prove convergence in norm and pointwise almost everywhere on$$L^p$$,$$p\in (1,\infty )$$, for certain multi-parameter polynomial ergodic averages by establishing the corresponding multi-parameter maximal and oscillation inequalities. Our result, in particular, gives an affirmative answer to a multi-parameter variant of the Bellow–Furstenberg problem. This paper is also the first systematic treatment of multi-parameter oscillation semi-norms which allows an efficient handling of multi-parameter pointwise convergence problems with arithmetic features. The methods of proof of our main result develop estimates for multi-parameter exponential sums, as well as introduce new ideas from the so-called multi-parameter circle method in the context of the geometry of backwards Newton diagrams that are dictated by the shape of the polynomials defining our ergodic averages. 

Abstract Identifying the migration routes and stopover sites used by declining species is critical for developing targeted conservation actions. Long-distance migratory shorebirds are among the groups of birds declining most rapidly, yet we frequently lack detailed knowledge about the routes and stopover sites they use during their hemisphere-spanning migrations. This is especially true for species that migrate through mid-continental regions in the Western Hemisphere. We therefore used satellite transmitters to track 212 individuals of 6 shorebird species during their southward migrations—Pluvialis dominica (American Golden-Plover), Limosa haemastica (Hudsonian Godwit), Tringa flavipes (Lesser Yellowlegs), and Calidris subruficollis (Buff-breasted Sandpiper), C. melanotos (Pectoral Sandpiper), and Bartramia longicauda (Upland Sandpiper)—as they crossed the Amazon Basin of South America, a region from which reports of shorebird numbers are increasing but remain relatively rare. Our results make clear that the Amazon Basin provides stopover habitat for a large number of shorebirds: more than 74% of individuals tracked crossing the Amazon Basin stopped over in the region for an average of 2–14 days, with some spending the entire nonbreeding season there. All species selected stopover sites along the region’s many rivers and lakes, while within stopover sites each species exhibited distinct habitat preferences. The timing of stopovers within sub-basins of the Amazon Basin also coincided with periods of low water, when the muddy, shallow water habitats preferred by most shorebirds are likely plentiful. Together, our results highlight the need for detailed investigations into shorebird abundance and distribution within the Amazon Basin, threats to shorebirds within particular subbasins, and links between shorebird conservation efforts and those targeting the myriad other species that inhabit this dynamic, hyper-diverse region. 

The local sum conjecture is a variant of some of Igusa’s questions on exponential sums put forward by Denef and Sperber. In a remarkable paper by Cluckers, Mustata and Nguyen, this conjecture has been established in all dimensions, using sophisticated, powerful techniques from a research area blending algebraic geometry with ideas from logic. The purpose of this paper is to give an elementary proof of this conjecture in two dimensions which follows Varčenko’s treatment of Euclidean oscillatory integrals based on Newton polyhedra for good coordinate choices. Another elementary proof is given by Veys from an algebraic geometric perspective. 

Abstract Submarine groundwater discharge is increasingly recognized as an important component of the oceanic geochemical budget, but knowledge of the distribution of this phenomenon is limited. To date, reports of meteoric inputs to marine sediments are typically limited to shallow shelf and coastal environments, whereas contributions of freshwater along deeper sections of tectonically active margins have generally been attributed to silicate diagenesis, mineral dehydration, or methane hydrate dissociation. Here, using geochemical fingerprinting of pore water data from Site J1003 recovered from the Chilean Margin during D/V JOIDES Resolution Expedition 379 T, we show that substantial offshore freshening reflects deep and focused contributions of meteorically modified geothermal groundwater, which is likely sourced from a reservoir ~2.8 km deep in the Aysén region of Patagonia and infiltrated marine sediments during or shortly after the last glacial period. Emplacement of fossil groundwaters reflects an apparently ubiquitous phenomenon in margin sediments globally, but our results now identify an unappreciated locus of deep submarine groundwater discharge along active margins with potential implications for coastal biogeochemical processes and tectonic instability. 

Abstract Sediment cores recently collected from the Chilean Margin during D/VJOIDES ResolutionExpedition 379T (JR100) document variability in shipboard‐generated records of the green/blue (G/B) ratio. These changes show a strong coherence with benthic foraminiferal δ¹⁸O, Antarctic ice core records, and sediment lithology (e.g., higher diatom abundances in greener sediment intervals), suggesting a climate‐related control on the G/B. Here, we test the utility of G/B as a proxy for diatom productivity at Sites J1002 and J1007 by calibrating G/B to measured biogenic opal. Strong exponential correlations between measured opal% and the G/B were found at both sites. We use the empirical regressions to generate high‐resolution records of opal contents (opal%) on the Chilean Margin. Higher productivity tends to result in more reducing sedimentary conditions. Redox‐sensitive sedimentary U/Th generally co‐varies with the reconstructed opal% at both sites, supporting the association between sediment color, sedimentary U/Th, and productivity. Lastly, we calculated opal mass accumulation rate (MAR) at Site J1007 over the last ∼150,000 years. The G/B‐derived opal MAR record from Site J1007 largely tracks existing records derived from traditional wet‐alkaline digestion from the south and eastern equatorial Pacific (EEP) Ocean, with a common opal flux peak at ∼50 ka suggesting that increased diatom productivity in the EEP was likely driven by enhanced nutrient supply from the Southern Ocean rather than dust inputs as previously suggested. Collectively, our results identify the G/B ratio as a useful tool with the potential to generate reliable, high‐resolution paleoceanographic records that circumvent the traditionally laborious methodology. 

The Arctic is entering a new ecological state, with alarming consequences for humanity. Animal-borne sensors offer a window into these changes. Although substantial animal tracking data from the Arctic and subarctic exist, most are difficult to discover and access. Here, we present the new Arctic Animal Movement Archive (AAMA), a growing collection of more than 200 standardized terrestrial and marine animal tracking studies from 1991 to the present. The AAMA supports public data discovery, preserves fundamental baseline data for the future, and facilitates efficient, collaborative data analysis. With AAMA-based case studies, we document climatic influences on the migration phenology of eagles, geographic differences in the adaptive response of caribou reproductive phenology to climate change, and species-specific changes in terrestrial mammal movement rates in response to increasing temperature.