Ghiyasi, A. H. Constants in inequalities for mean values of some periodic arithmetic functions. (English. Russian original) Zbl 1304.11085 Mosc. Univ. Math. Bull. 63, No. 6, 265-269 (2008); translation from Vest. Mosk. Univ. Mat. Mekh. 63, No. 6, 44-48 (2008). Summary: Constants in estimates of short Gaussian sums and sums of products of Legendre symbols over sequences of natural numbers shifted by various numbers are refined. MSC: 11L40 Estimates on character sums 11L07 Estimates on exponential sums PDF BibTeX XML Cite \textit{A. H. Ghiyasi}, Mosc. Univ. Math. Bull. 63, No. 6, 265--269 (2008; Zbl 1304.11085); translation from Vest. Mosk. Univ. Mat. Mekh. 63, No. 6, 44--48 (2008) Full Text: DOI References: [1] I. M. Vinogradov, ”Sur la Distribution des Residues et des Nonresidues des Puissances,” Zh. Fiz.-Matem. Obshch. Perm’ Gos. Univ. 1, 94 (1918). [2] I. M. Vinogradov, ”Distribution of Quadratic Residues and Nonresidues,” Zh. Fiz.-Matem. Obshch. Perm’ Gos. Univ. 2, 1 (1919). [3] I. M. Vinogradov, Foundations of the Theory of Numbers, 9th ed. (Nauka, Moscow, 1981; 6th ed. Pergamon Press, New York, 1955). [4] G. Pólya, ”Über die Verteilung der quadratischen Reste und Nichtreste,” in Nachr. Königl. Ges. Wiss. (Göttingen, 1918), pp. 21–29. · JFM 46.0265.02 [5] E. Landau, ”Abschätzungen von Charactersummen, Einheiten und Klassenzahlen,” in Nachr. Königl. Ges. Wiss. (Göttingen, 1918), pp. 79–97. [6] D. A. Burgess, ”The Distribution of Quadratic Residues and Nonresidues,” Mathematika 4(8), 106 (1957). · Zbl 0081.27101 [7] D. A. Burgess, ”On Character Sums and L-Series,” Proc. London Math. Soc. (3) 12, 193 (1962). · Zbl 0106.04004 [8] D. A. Burgess, ”On Character Sums and L-Series, II,” Proc. London Math. Soc. (3) 13, 524 (1963). · Zbl 0123.04404 [9] D. A. Burgess, ”The Character Sum Estimate with r = 3,” J. London Math. Soc. 33, 219 (1986). · Zbl 0593.10033 [10] H. L. Montgomery and R. C. Vaughan, ”Exponential Sums with Multiplicative Coefficients,” Invent. math. 43, 69 (1977). · Zbl 0362.10036 [11] A. Hildebrand, ”On the Constant in the Pólya-Vinogradov Inequality,” Can. Math. Bull. 3, 347 (1988). · Zbl 0612.10033 [12] A. Hildebrand, ”Large Values of Character Sums,” J. Number Theory 29, 271 (1988). · Zbl 0652.10029 [13] H. L. Montgomery, Topics in Multiplicative Number Theory (Springer-Verlag, Berlin, 1971; Mir, Moscow, 1974). · Zbl 0216.03501 [14] R. E. A. C. Paley, ”A Theorem on Characters,” J. London Math. Soc. 7, 28 (1932). · Zbl 0003.34101 [15] G. Pólya and G. Szego, Problems and Theorems in Analysis I, II (Springer-Verlag, N.Y., 1976; Nauka, Moscow, 1978). [16] G. I. Arkhipov, V. A. Sadovnichii, and V. N. Chubarikov, Lectures in Mathematical Analysis, 5th ed. (Drofa, Moscow, 2005) [in Russian]. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.