메뉴 건너뛰기




Volumn 103, Issue 2, 2003, Pages 267-280

Spectra of certain types of polynomials and tiling of integers with translates of finite sets

Author keywords

Cyclotomic polynomials; Spectrum of a polynomial; Tiling

Indexed keywords


EID: 0346273564     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnt.2003.06.006     Document Type: Article
Times cited : (20)

References (25)
  • 1
    • 0033072695 scopus 로고    scopus 로고
    • Tiling the integers with translates of one finite set
    • E. Coven, A. Meyerowitz, Tiling the integers with translates of one finite set, J. Algebra 212 (1999) 161-174.
    • (1999) J. Algebra , vol.212 , pp. 161-174
    • Coven, E.1    Meyerowitz, A.2
  • 2
    • 0000758425 scopus 로고
    • Commuting self-adjoint partial differential operators and a group-theoretic problem
    • B. Fuglede, Commuting self-adjoint partial differential operators and a group-theoretic problem, J. Funct. Anal. 16 (1974) 101-121.
    • (1974) J. Funct. Anal. , vol.16 , pp. 101-121
    • Fuglede, B.1
  • 3
    • 0010996422 scopus 로고    scopus 로고
    • A characterization of finite sets that tile the integers
    • preprint
    • A. Granville, I. Łaba, Y. Wang, A characterization of finite sets that tile the integers, preprint, 2001.
    • (2001)
    • Granville, A.1    Łaba, I.2    Wang, Y.3
  • 4
    • 0033244185 scopus 로고    scopus 로고
    • Fourier bases and a distance problem of Erdös
    • A. Iosevich, N.H. Katz, S. Pedersen, Fourier bases and a distance problem of Erdös, Math. Res. Lett. 6 (1999) 251-255.
    • (1999) Math. Res. Lett. , vol.6 , pp. 251-255
    • Iosevich, A.1    Katz, N.H.2    Pedersen, S.3
  • 5
    • 0001678028 scopus 로고    scopus 로고
    • Convex bodies with a point of curvature do not have Fourier bases
    • A. Iosevich, N.H. Katz, T. Tao, Convex bodies with a point of curvature do not have Fourier bases, Amer. J. Math. 123 (2001) 115-120.
    • (2001) Amer. J. Math. , vol.123 , pp. 115-120
    • Iosevich, A.1    Katz, N.H.2    Tao, T.3
  • 6
    • 0011011360 scopus 로고    scopus 로고
    • Fuglede conjecture holds for convex planar domains
    • preprint
    • A. Iosevich, N.H. Katz, T. Tao, Fuglede conjecture holds for convex planar domains, preprint, 2001.
    • (2001)
    • Iosevich, A.1    Katz, N.H.2    Tao, T.3
  • 7
    • 1842729485 scopus 로고    scopus 로고
    • Spectral and tiling properties of the unit cube
    • A. Iosevich, S. Pedersen, Spectral and tiling properties of the unit cube, Internat. Math. Res. Notices 16 (1998) 819-828.
    • (1998) Internat. Math. Res. Notices , vol.16 , pp. 819-828
    • Iosevich, A.1    Pedersen, S.2
  • 8
    • 0011041049 scopus 로고
    • Fractal geometry and stochastics
    • Birkhäuser, Basel
    • P. Jorgensen, S. Pedersen, Fractal geometry and stochastics, in: Progress in Probability, Vol. 17, Birkhäuser, Basel, 1995, pp. 191-219.
    • (1995) Progress in Probability , vol.17 , pp. 191-219
    • Jorgensen, P.1    Pedersen, S.2
  • 9
  • 10
    • 0001519206 scopus 로고
    • Über die lückenlose Einfüllung des Raumes mit Würfeln
    • O.H. Keller, Über die lückenlose Einfüllung des Raumes mit Würfeln, J. Reine Angew. Math. 163 (1930) 231-248.
    • (1930) J. Reine Angew. Math. , vol.163 , pp. 231-248
    • Keller, O.H.1
  • 11
    • 0034259257 scopus 로고    scopus 로고
    • Nonsymmetric convex domains have no basis of exponentials
    • M. Kolountzakis, Nonsymmetric convex domains have no basis of exponentials, Illinois J. Math. 44 (2000) 542-550.
    • (2000) Illinois J. Math. , vol.44 , pp. 542-550
    • Kolountzakis, M.1
  • 12
    • 0034259550 scopus 로고    scopus 로고
    • Packing, tiling, orthogonality, and completeness
    • M. Kolountzakis, Packing, tiling, orthogonality, and completeness, Bull. London Math. Soc. 32 (2000) 589-599.
    • (2000) Bull. London Math. Soc. , vol.32 , pp. 589-599
    • Kolountzakis, M.1
  • 13
    • 0011020286 scopus 로고    scopus 로고
    • A class of nonconvex polytopes that admit no orthogonal basis of exponentials
    • preprint
    • M. Kolountzakis, M. Papadimitrakis, A class of nonconvex polytopes that admit no orthogonal basis of exponentials, preprint, 2001.
    • (2001)
    • Kolountzakis, M.1    Papadimitrakis, M.2
  • 14
    • 23044531025 scopus 로고    scopus 로고
    • Fuglede's conjecture for a union of two intervals
    • I. Łaba, Fuglede's conjecture for a union of two intervals, Proc. Amer. Math. Soc. 129 (2001) 2965-2972.
    • (2001) Proc. Amer. Math. Soc. , vol.129 , pp. 2965-2972
    • Łaba, I.1
  • 15
    • 0036401715 scopus 로고    scopus 로고
    • The spectral set conjecture and multiplicative properties of roots of polynomials
    • I. Łaba, The spectral set conjecture and multiplicative properties of roots of polynomials, J. London Math. Soc. 65 (2002) 661-671.
    • (2002) J. London Math. Soc. , vol.65 , pp. 661-671
    • Łaba, I.1
  • 16
    • 0002355528 scopus 로고    scopus 로고
    • Orthonormal bases of exponentials for the n-cube
    • J.C. Lagarias, J.A. Reed, Y. Wang, Orthonormal bases of exponentials for the n-cube, Duke Math. J. 103 (2000) 25-37.
    • (2000) Duke Math. J. , vol.103 , pp. 25-37
    • Lagarias, J.C.1    Reed, J.A.2    Wang, Y.3
  • 17
    • 0035594102 scopus 로고    scopus 로고
    • Universal spectra and Tijdeman's conjecture on factorization of cyclic groups
    • J.C. Lagarias, S. Szabó, Universal spectra and Tijdeman's conjecture on factorization of cyclic groups, J. Fourier Anal. Appl. 7 (2001) 63-70.
    • (2001) J. Fourier Anal. Appl. , vol.7 , pp. 63-70
    • Lagarias, J.C.1    Szabó, S.2
  • 18
    • 0031115862 scopus 로고    scopus 로고
    • Spectral sets and factorizations of finite abelian groups
    • J.C. Lagarias, Y. Wang, Spectral sets and factorizations of finite abelian groups, J. Funct. Anal. 145 (1997) 73-98.
    • (1997) J. Funct. Anal. , vol.145 , pp. 73-98
    • Lagarias, J.C.1    Wang, Y.2
  • 19
    • 0002727874 scopus 로고
    • Tesselation of integers
    • D.J. Newman, Tesselation of integers, J. Number Theory 9 (1977) 107-111.
    • (1977) J. Number Theory , vol.9 , pp. 107-111
    • Newman, D.J.1
  • 20
    • 0030295762 scopus 로고    scopus 로고
    • Spectral sets whose spectrum is a lattice with a base
    • S. Pedersen, Spectral sets whose spectrum is a lattice with a base, J. Funct. Anal. 141 (1996) 496-509.
    • (1996) J. Funct. Anal. , vol.141 , pp. 496-509
    • Pedersen, S.1
  • 21
    • 25044452165 scopus 로고    scopus 로고
    • The dual spectral set conjecture
    • preprint
    • S. Pedersen, The dual spectral set conjecture, preprint, 2002.
    • (2002)
    • Pedersen, S.1
  • 22
    • 0035538497 scopus 로고    scopus 로고
    • Universal spectra, universal tiling sets, and the spectral set conjecture
    • S. Pedersen, Y. Wang, Universal spectra, universal tiling sets, and the spectral set conjecture, Math. Scand. 88 (2001) 246-256.
    • (2001) Math. Scand. , vol.88 , pp. 246-256
    • Pedersen, S.1    Wang, Y.2
  • 23
    • 84971915495 scopus 로고
    • On Keller's conjecture for certain cyclic groups
    • A. Sands, On Keller's conjecture for certain cyclic groups, Proc. Edinburgh Math. Sec. 2 (1979) 17-21.
    • (1979) Proc. Edinburgh Math. Sec. , vol.2 , pp. 17-21
    • Sands, A.1
  • 24
    • 0037910186 scopus 로고    scopus 로고
    • Replacement of factors by subgroups in the factorization of abelian groups
    • A. Sands, Replacement of factors by subgroups in the factorization of abelian groups, Bull. London Math. Soc. 32 (2000) 297-304.
    • (2000) Bull. London Math. Soc. , vol.32 , pp. 297-304
    • Sands, A.1
  • 25
    • 0010811775 scopus 로고
    • Decomposition of the integers as a direct sum of two subsets
    • London Mathematical Society Lecture Notes, Cambridge University Press, Cambridge
    • R. Tijdeman, Decomposition of the integers as a direct sum of two subsets, in: Number Theory (Paris 1992-1993), London Mathematical Society Lecture Notes, Vol. 215, Cambridge University Press, Cambridge, 1995, pp. 261-276.
    • (1995) Number Theory (Paris 1992-1993) , vol.215 , pp. 261-276
    • Tijdeman, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.