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Statistical Distribution of Roots of a Polynomial Modulo Primes II

References [1] KITAOKA,Y.: Statistical distribution of roots of a polynomial modulo primes, (submitted). [2] The On-Line Encyclopedia of Integer Sequences, Published electronically, 2000, [3] SERRE, J. P.: Quelques applications du théorème de densité de Chebotarev, I.H.E.S., 54 (1981), 323-401.

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Uniform Distribution with Respect to Density

References BINDER, C.: Über einen Satz von de Bruijn und Post, ¨Osterr. Akad. Wiss. Math.-Naturw. Kl. SB. II, 179 (1971), 233-251. DE BRUIJN, N.G.-POST, K. A.: A remark on uniformly distributed sequences and Riemann integrability Indag. Math. 30 (1968), 149-150. BUCK, R. C.: The measure theoretic approach to density, Amer. J. Math 68 (1946), 560-580. CRISTEA, L. L.-PRODINGER, H.: Moments of distributions related to digital expansions, J. Math. Anal. Appl. 315 (2006), 606

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On Small Sets of Distribution Functions of Ratio Block Sequences

REFERENCES [FT] FILIP, F.—TÓTH, J. T.: Characterization of asymptotic distribution functions of ratio block sequences , Periodica Mathematica Hungarica 60 (2010), no. 2, 115–126. [GS] G: REKOS, G.—STRAUCH, O. Distribution functions of ratio sequences, II , Unif. Distrib. Theory 2 (2007), no. 1, 53–77. [GV] GREKOS, G.—VOLKMANN, B.: On densities and gaps , Journal of Number Theory 26 (1987), 129–148. [Po] PÓLYA, G.: Untersuchungen über Lücken und Singularitäten von Potenzreihen , Math. Zeit. 29 (1929), 549–640. [SN] STRAUCH

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Distribution of Leading Digits of Numbers

REFERENCES [1] BAKER, R. C.—HARMAN, G.—PINTZ, J.: The difference between consecutive primes, II , Proc. London Math. Soc. (3) 83 (2001), no. 3, 532–562. [2] BALÁŽ, V.—NAGASAKA, K.—STRAUCH, O.: Benford’s law and distribution functions of sequences in (0, 1) (Russian), Mat. Zametki 88 (2010), no. 4, 485–501; (English translation) Math. Notes 88 (2010), no. 4, 449–463. [3] BENFORD, F.: The law of anomalous numbers , Proc. Amer. Phil. Soc. 78 (1938), 551–572 (Zbl 18, 265; JFM 64.0555.03). [4] DIACONIS, P.: The distribution of

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Optimal Quantization for Piecewise Uniform Distributions

REFERENCES [AW] ABAYA, E. F.—WISE, G. L.: Some remarks on the existence of optimal quantizers , Statistics & Probability Letters 2 (1984), no. 6, 349–351. [C] CHUNG, K.-L.: An estimate concerning the Kolmogoroff limits distribution , Trans. Amer. Math. Soc. 67 (1949), 36–50. [PC] COHORT, P.: Limit theorems for random normalized distortion , Ann. Appl. Probab. 14 (2004), no. 1, 118–143. [D] DEHEUVELS, P.: Strong bounds for multidimensional spacings , Z. Wahrsch. Verw. Gebiete 64 (1983, 411–424. [DR] DETTMANN, C. P

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On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, I. (General Results)

References [1] AISTLEITNER, C.: On the limit distribution of the well-distribution measure of random binary sequences, J. Thor. Nombres Bordeaux 25 (2013), no. 2, 245-259. [2] ALON, N.-KOHAYAKAWA, Y.- MAUDUIT, C.-MOREIRA, C. G. - RÖDL, C. G.: Measures of pseudorandomness for finite sequences: typical values, Proc. Lond. Math. Soc. 95 (2007), 778-812. [3] BECK, J.: Roth’s estimate of the discrepancy of integer sequences is nearly sharp, Combinatorica 1 (1981), 319-325. [4] BECK, J.-SÁRKÖZY, A

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An Extremal Problem in Uniform Distribution Theory

REFERENCES [1] BALÁŽ, V.—MIŠÍK, L.—STRAUCH, O.—TÓTH, J. T.: Distribution functions of ratio sequences, III, Publ. Math. Debrecen 82 (2013), no. 3-4, 511-529. [2] _____ Distribution functions of ratio sequences, IV , Period. Math. Hungar. 66 (2013) no. 1, 1-22. [3] BEIGLBÖCK, M.—HENRY-LABORDÈRE, P.—PENKNER, F.: Model-independent bounds for option prices—a mass transport approach, Finance Stoch. 17 (2013), no. 3, 477-501. [4] BOSCH, W.: Functions that preserve the uniform distribution of sequences, Trans. Amer. Math. Soc. 307

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Notes on the Distribution of Roots Modulo a Prime of a Polynomial

, Osaka J. Math. 49 (2012), 393-420. [6] Statistical distribution of roots of a polynomial modulo prime powers, In: Number Theory: Plowing and Starring through High Wave Forms, Ser. Number Theory Appl. Vol. 11, 2015, World Sci. publ., Hackensack, NJ, pp. 75-94. [7] Statistical distribution of roots of a polynomial modulo primes, (submitted). [8] Y. KITAOKA: Statistical distribution of roots of a polynomial modulo primes II, Unif. Distrib. Theory 12 (2017), no. 1, 109-122. [9] TÓTH, T. ´A.: Roots of

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Distribution Functions for Subsequences of Generalized Van Der Corput Sequences

References [AH] AISTLEITNER, C.-HOFER, M.: On the limit distribution of consequtive elements of the van der Corput sequence, Unif. Distrib. Theory 8 (2013), no. 1, 89-96. [AN] ASMAR, N. H.-NAIR, R.: Certain averages on the a-adic numbers, Proc. Amer. Math. Soc. 114 (1992) no. 1, 21-28. [B] BRAUER, A.: On algebraic equations with all but one root in the interior of the unit circle, Math. Nachr. 4, (1951) 250-257. [CFS] CORNFELD, I. P.-FORMIN, S. V.-SINAI, YA. G.: Ergodic Theory, Springer

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On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, II (Constructive Bounds)

REFERENCES [1] BURGESS, D. A.: On character sums and primitive roots , Proc. London Math. Soc. 1 2 (1962), no. 3, 179–192. [2] DARTYGE, C.—GYARMATI, K.—SÁRKÖZY, A.: On irregularities of distribution of binary sequences relative to arithmetic progressions, I. (General results) , Unif. Distrib. Theory 1 2 (2017), no. 1, 55–67. [3] DAVENPORT, H.—ERDŐS, P.: The distribution of quadratic and higher residues , Publ. Math. Debrecen 2 (1952), 252–265. [4] ERDŐS, P.—SÁRKÖZY, A.: Some solved and unsolved problems in combinatorial number

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