In this paper, we propose a novel method using elementary number theory to
investigate the discrete nature of the screw dislocations in crystal lattices, namely the
simple cubic (SC) lattice and body-centered cubic (BCC) lattice, by developing the
algebraic description of the dislocations in the previous report of Hamada,
Matsutani, Nakagawa, Saeki, and Uesaka (Pac. J. Math. Ind. 10 (2018),
art. id. 3). Using this method, we showed that the stress energy of the screw
dislocations in the BCC lattice and the SC lattice are naturally described; the
energy of the BCC lattice was expressed by the truncated Epstein–Hurwitz
zeta function of the Eisenstein integers, whereas that of the SC lattice is
associated with the truncated Epstein–Hurwitz zeta function of the Gauss
integers.
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