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1. CJM 2010 (vol 63 pp. 38)

Brüdern, Jörg; Wooley, Trevor D.
 Asymptotic Formulae for Pairs of Diagonal Cubic Equations We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system. Keywords:exponential sums, Diophantine equationsCategories:11D72, 11P55

2. CJM 2009 (vol 61 pp. 336)

Garaev, M. Z.
 The Large Sieve Inequality for the Exponential Sequence $\lambda^{[O(n^{15/14+o(1)})]}$ Modulo Primes Let $\lambda$ be a fixed integer exceeding $1$ and $s_n$ any strictly increasing sequence of positive integers satisfying $s_n\le n^{15/14+o(1)}.$ In this paper we give a version of the large sieve inequality for the sequence $\lambda^{s_n}.$ In particular, we obtain nontrivial estimates of the associated trigonometric sums on average" and establish equidistribution properties of the numbers $\lambda^{s_n} , n\le p(\log p)^{2+\varepsilon}$, modulo $p$ for most primes $p.$ Keywords:Large sieve, exponential sumsCategories:11L07, 11N36