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 2012, Volume 276

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Number theory, algebra, and analysis

Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday

 Anatolii Alekseevich Karatsuba (photo) Anatolii Alekseevich Karatsuba (1937–2008) 7 On the law of the iterated logarithm for permuted lacunary sequencesC. Aistleitner, I. Berkes, R. Tichy 9 $q$-Orthogonal polynomials, Rogers–Ramanujan identities, and mock theta functionsGeorge E. Andrews 27 Elementary remarks on Möbius' functionMichel Balazard 39 Fundamental solutions to Pell equation with prescribed sizeÉtienne Fouvry, Florent Jouve 46 On the distribution of values of the derivative of the Riemann zeta function at its zeros. IAkio Fujii 57 Asymptotics for the sum of powers of distances between power residues modulo a primeM. Z. Garaev, S. V. Konyagin, Yu. V. Malykhin 83 On an additive problem and its application to the problem of distribution of zeros of linear combinations of Hecke $L$-functions on the critical lineS. A. Gritsenko 96 Application of an idea of Voronoĭ to lattice zeta functionsPeter M. Gruber 109 Identities involving Farey fractionsM. N. Huxley 131 On the general additive divisor problemAleksandar Ivić, Jie Wu 146 Transformations of zeta-sumsMatti Jutila 155 On Karatsuba's problem related to Gram's lawM. A. Korolev 162 On universality of the Lerch zeta-functionA. Laurinčikas 173 Enlarged major arcs in additive problems. IIJianya Liu 182 Diophantine approximation generalizedLadislav Mišík, Oto Strauch 198 Jacob's ladders, the structure of the Hardy–Littlewood integral and some new class of nonlinear integral equationsJan Moser 213 Are there arbitrarily long arithmetic progressions in the sequence of twin primes? IIJános Pintz 227 An extension of Motohashi's observation on the zero-free region of the Riemann zeta-functionSergei N. Preobrazhenskiĭ 233 On the multiplicity of solutions of a system of algebraic equationsA. V. Pukhlikov 239 Equal values of trinomials revisitedA. Schinzel 255 A note on the distribution of some additive functionsGérald Tenenbaum 262 On the remainder term in the circle problem in an arithmetic progressionD. I. Tolev 266 Geometric proof of Rødseth's formula for Frobenius numbersA. V. Ustinov 280