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Metaharmonic Lattice Point Theory (Paperback)
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Metaharmonic Lattice Point Theory (Paperback)
Series: Chapman & Hall Pure and Applied Mathematics
Expected to ship within 12 - 19 working days
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Metaharmonic Lattice Point Theory covers interrelated methods and
tools of spherically oriented geomathematics and periodically
reflected analytic number theory. The book establishes
multi-dimensional Euler and Poisson summation formulas
corresponding to elliptic operators for the adaptive determination
and calculation of formulas and identities of weighted lattice
point numbers, in particular the non-uniform distribution of
lattice points. The author explains how to obtain multi-dimensional
generalizations of the Euler summation formula by interpreting
classical Bernoulli polynomials as Green's functions and linking
them to Zeta and Theta functions. To generate multi-dimensional
Euler summation formulas on arbitrary lattices, the Helmholtz wave
equation must be converted into an associated integral equation
using Green's functions as bridging tools. After doing this, the
weighted sums of functional values for a prescribed system of
lattice points can be compared with the corresponding integral over
the function. Exploring special function systems of Laplace and
Helmholtz equations, this book focuses on the analytic theory of
numbers in Euclidean spaces based on methods and procedures of
mathematical physics. It shows how these fundamental techniques are
used in geomathematical research areas, including gravitation,
magnetics, and geothermal.
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