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 2010, Volume 88, Issue 4

 Anatolii Alekseevich Karatsuba (photo) Benford's Law and Distribution Functions of Sequences in $(0,1)$V. Baláž, K. Nagasaka, O. Strauch 485 Proof of the Faugère Criterion for the F5 AlgorithmO. N. German 502 On Algebraic Identities between Generalized Hypergeometric FunctionsV. A. Gorelov 511 On a Problem of KaratsubaS. A. Gritsenko 517 Estimates of Character Sums in Finite FieldsS. V. Konyagin 529 Alternatives to the Euler–Maclaurin Formula for Calculating Infinite SumsYu. V. Matiyasevich 543 On the Irrationality Exponent of the Number $\ln2$Yu. V. Nesterenko 549 Two Modularity Lifting Conjectures for Families of Siegel Modular FormsA. A. Panchishkin 565 Existence of the Kähler–Einstein Metric on Certain Fano Complete IntersectionsA. V. Pukhlikov 575 On the Measure of Irrationality of the Number $\pi$V. Kh. Salikhov 583 The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete QuotientsA. V. Ustinov 594 Character Sums over Shifted PrimesJ. B. Friedlander, K. Gong, I. E. Shparlinski 605 A Supercongruence Motivated by the Legendre Family of Elliptic CurvesHeng Huat Chan, Ling Long, W. Zudilin 620 On Monochromatic Solutions of Some Nonlinear Equations in $\mathbb Z/p\mathbb Z$I. D. Shkredov 625 The Mellin Transform of Hardy's Function is EntireM. Jutila 635 Corrections 640
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