The Pólya-Vinogradov inequality for totally real algebraic number fields

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K. M. Bartz, On a theorem of A. V. Sokolovskiĭ, Acta Arith. 34 (1978), 113-126.
G. H. Hardy and J. E. Littlewood, Some problems of Diophantine approximation: The lattice-points of a right-handed triangle, Proc. London Math. Soc. (2) 20 (1921), 15-36.
J. G. Hinz, Character sums in algebraic number fields, J. Number Theory 17 (1983), 52-70.
K. C. Lee, On the average order of characters in totally real algebraic number fields, Chinese J. Math. 7 (1979), 77-90.
K. Mahler, Inequalities for ideal bases in algebraic number fields, J. Austral. Math. Soc. 4 (1964), 425-448.
H. L. Montgomery and R. C. Vaughan, Mean values of character sums, Canad. J. Math. 31 (1979), 476-487.
G. Pólya, Über die Verteilung der quadratischen Reste und Nichtreste, Göttinger Nachr. (1918), 21-29.
U. Rausch, Character sums in algebraic number fields, to appear.
G. J. Rieger, Verallgemeinerung der Siebmethode von A. Selberg auf algebraische Zahlkörper. III, J. Reine Angew. Math. 208 (1961), 79-90.
M. M. Skriganov, Lattices in algebraic number fields and uniform distribution mod 1, Leningrad Math. J. 1 (1990), 535-558.
D. C. Spencer, The lattice points of tetrahedra, J. Math. Phys. 21 (1942), 189-197.
T. Tatuzawa, Fourier analysis used in analytic number theory, Acta Arith. 28 (1975), 263-272