p-Bessel functions receive a hierarchical structure from fractional derivatives, explicit integral representations, and complex extensions as new oscillatory kernels for anisotropic domains.
Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic
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abstract
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few years. It deals with the classic circle and sphere problems, as well as with the present state-of-the-art concerning lattice points in more general regions and bodies. Furthermore, a thorough account is given on divisor problems and related arithmetic functions.
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2026 2verdicts
UNVERDICTED 2representative citing papers
Explicit dimension-dependent upper bounds on logarithmic codebook size for high-dimensional signal compression are obtained by refining Landau's lattice point estimates via uniform Bessel bounds and Abel summation.
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Analytic Study of $p$-Bessel Functions: Fractional Calculus, Integral Representations, and Complex Extensions
p-Bessel functions receive a hierarchical structure from fractional derivatives, explicit integral representations, and complex extensions as new oscillatory kernels for anisotropic domains.
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High-Dimensional Signal Compression: Lattice Point Bounds and Metric Entropy
Explicit dimension-dependent upper bounds on logarithmic codebook size for high-dimensional signal compression are obtained by refining Landau's lattice point estimates via uniform Bessel bounds and Abel summation.