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Let (?(f) (n))(n=1) be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f. We prove that, for any fixed ? > 0, under the Ramanujan-Petersson conjecture for GL(2) Maass forms, the Rankin-Selberg coefficients (?(f) ...
We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...
More than a century has passed since pathological protein aggregates were first identified in the brains of patients with neurodegenerative diseases (NDDs). Yet, we still do not have effective therapies to treat or slow the progression of these devastating ...
This dataset contains equivalent black carbon (eBC) concentrations, averaged to 10 min time resolution, measured during the year-long MOSAiC expedition from October 2019 to September 2020. The measurements were performed in the Swiss container on the D-dec ...
A decomposition of multicorrelation sequences for commuting transformations along primes, Discrete Analysis 2021:4, 27 pp. Szemerédi's theorem asserts that for every positive integer k and every δ>0 there exists n such that every subset of ${1, ...
We investigate how spectral properties of a measure-preserving system (X, B, mu, T) are reflected in the multiple ergodic averages arising from that system. For certain sequences a :N -> N, we provide natural conditions on the spectrum sigma (T) such that, ...
Considering brain structural alterations as neurodegenerative consequences of Parkinson's disease (PD), we sought to infer the progression of PD via the ordering of brain structural alterations from cross-sectional MRI observations. Having measured cortica ...
This dataset contains aerosol optical absorption coefficients at seven different wavelengths (babs(λ)), averaged to 10 min time resolution, measured during the year-long MOSAiC expedition from October 2019 to September 2020. The measurements were performed ...
We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. First, we show that a symmetric set S subset of Z(q)(n) containing vertical bar S vertical bar = mu . q(n) elements must contain at leas ...
Between 1672 and 1694, the German mathematician Gottfried Wilhelm Leibniz (1646-1716) attempted to design a reckoning machine that would be able to perform the four basic arithmetic operations on multiple-digit numbers. Working closely with the French cloc ...