A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem
Mathematika, Volume 70, Issue 1, January 2024.Abstract We interpret into decoupling language a refinement of a 1973 argument due to Karatsuba on Vinogradov's mean value theorem. The main goal of our argument is to answer what precisely solution counting in older partial progress on Vinogradov's mean value theorem corresponds to in Fourier decoupling theory.
Brian Cook +5 more
wiley +1 more source
, 2009 The thesis gave a fine study on the distribution of the coefficients of automorphic L-functions for GL(m) with m>1. In particular we have treated two types of problems: change of signs of these coefficients (when they are real) and their decompensation on the prime numbers.
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Advancing full-field metrology: rapid 3D imaging with geometric phase ferroelectric liquid crystal technology in full-field optical coherence microscopy. [PDF]
Biomed Opt Express, 2023 Zheng W, Kou SS, Sheppard CJR, Roy M.
europepmc +1 more source
Integration of Carbon Nanotubes in an HFCVD Diamond Synthesis Process in a Methane-Rich H2/CH4 Gas Mixture. [PDF]
Materials (Basel), 2023 Mitulinsky A +5 more
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THE GOLDBACH-LINNIK PROBLEM: SOME CONDITIONAL RESULTS
, 2011 This work concerns the Goldbach-Linnik problem, which is a variation of Goldbach's one: here the goal is to prove that all large even integers can be written as a sum of two primes and k powers of 2, where k is a fixed positive integer. Assuming the Generalized Riemann Hypothesis, first we prove two results on the size of the exceptional set of the ...
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Ultrafast magnetoacoustics in Galfenol nanostructures. [PDF]
Photoacoustics, 2023 Scherbakov AV +7 more
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A de Bruijn identity for symmetric stable laws
, 2013 We show how some attractive information--theoretic properties of Gaussians pass over to more general families of stable densities. We define a new score function for symmetric stable laws, and use it to give a stable version of the heat equation.
Johnson, Oliver
core
Characterization of Functional Materials Using Coherence Scanning Interferometry and Environmental Chambers. [PDF]
ACS Omega, 2023 Montgomery PC +11 more
europepmc +1 more source
Goldbach–Linnik–Type Problem of Symmetric Mixed Powers of Primes and Powers of Two
SymmetryThis article demonstrates that every sufficiently large odd integer can be expressed as the sum of one square of a prime, six cubes of primes, and 23 powers of two. This finding represents an improvement on the previous results of Sinnadurai in 1965 and Hooley in 1981.
Fei Xue +3 more
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Linnik problem for Maass--Hecke cuspforms and effective multiplicity one theorem
We investigate two related problems concerning the dimension of joint eigenspaces of the Laplace--Beltrami operator and a finite set of Hecke operators on $\mathbb{X}=\mathrm{PGL}_2(\mathbb{Z})\backslash \mathbb{H}$. First, we consider Linnik problem for Maass--Hecke cuspforms.
Jung, Junehyuk, Lee, Min
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