Bibliography
I. M. Vinogradov, Selected Works [in Russian], Izd. AN SSSR, Moscow, 1952.
I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory [in Russian], 2nd edition, Nauka, Moscow, 1980.
I. M. Vinogradov, Special Versions of the Method of Trigonometric Sums [in Russian], Nauka, Moscow, 1976.
A. A. Karatsuba Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 59 (1995), no. 4, 61–80.
A. A. Karatsuba Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 59 (1995), no. 5, 93–102.
J. Friedlander and H. Iwaniec, The Brun-Titchmarsh Theorem, Lecture Notes in Statist., vol. 247, Cambridge Univ. Press, Cambridge, 1997.
S. Konyagin and I. Shparlinski, Character Sums with Exponential Functions, Cambridge Univ. Press, Cambridge, 1999.
S. V. Konyagin in: IV International Conference “Problems of Current Interest in Number Theory and its Applications”, Topical Problems, pt. III [in Russian], Moscow, 2002, pp. 86–114.
D. R. Heath-Brown and S. V. Konyagin Quart. J. Math., 51 (2000), 221–235.
Yu. V. Malykhin, “Estimates of trigonometric sums modulo p 2,” (to appear).
J. Bourgain and S. V. Konyagin C. R. Math. Acad. Sci. Paris, 337 (2003), no. 2, 75–80.
J. Bourgain and Mei-Chu Chang C. R. Math. Acad. Sci. Paris, 339 (2004), no. 7, 463–466.
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Translated from Matematicheskie Zametki, vol. 80, no. 5, 2006, pp. 793–796.
Original Russian Text Copyright © 2006 by Yu. V. Malykhin.
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Malykhin, Y.V. Estimates of trigonometric sums modulo p r . Math Notes 80, 748–752 (2006). https://doi.org/10.1007/s11006-006-0197-1
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DOI: https://doi.org/10.1007/s11006-006-0197-1