The Pólya-Vinogradov inequality for totally real algebraic number fields

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1. [1] K. M. Bartz, On a theorem of A. V. Sokolovskiĭ, Acta Arith. 34 (1978), 113-126. Zbl0333.12008
2. [2] 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. Zbl48.0197.07
3. [3] J. G. Hinz, Character sums in algebraic number fields, J. Number Theory 17 (1983), 52-70. Zbl0511.10028
4. [4] K. C. Lee, On the average order of characters in totally real algebraic number fields, Chinese J. Math. 7 (1979), 77-90. Zbl0423.12003
5. [5] K. Mahler, Inequalities for ideal bases in algebraic number fields, J. Austral. Math. Soc. 4 (1964), 425-448. Zbl0218.12004
6. [6] H. L. Montgomery and R. C. Vaughan, Mean values of character sums, Canad. J. Math. 31 (1979), 476-487. Zbl0416.10030
7. [7] G. Pólya, Über die Verteilung der quadratischen Reste und Nichtreste, Göttinger Nachr. (1918), 21-29. Zbl46.0265.02
8. [8] U. Rausch, Character sums in algebraic number fields, to appear. Zbl0795.11033
9. [9] G. J. Rieger, Verallgemeinerung der Siebmethode von A. Selberg auf algebraische Zahlkörper. III, J. Reine Angew. Math. 208 (1961), 79-90. 
10. [10] M. M. Skriganov, Lattices in algebraic number fields and uniform distribution mod 1, Leningrad Math. J. 1 (1990), 535-558. Zbl0714.11045
11. [11] D. C. Spencer, The lattice points of tetrahedra, J. Math. Phys. 21 (1942), 189-197. Zbl0060.11501
12. [12] T. Tatuzawa, Fourier analysis used in analytic number theory, Acta Arith. 28 (1975), 263-272 Zbl0279.42024