Journal ArticleDOI
Basic analytic number theory, by A. A. Karatsuba. Pp 222. DM 148. 1993. ISBN 3-540-53345-1 (Springer)
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This article is published in The Mathematical Gazette.The article was published on 1995-03-01. It has received 34 citations till now. The article focuses on the topics: Karatsuba algorithm.read more
Citations
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The gcd-sum function
TL;DR: The Dirichlet series has a compact representation in terms of the Riemann zeta function as mentioned in this paper, and asymptotic forms for values of partial sums at real values are derived, including estimates for error terms.
Journal ArticleDOI
On the logarithmic factor in error term estimates in certain additive congruence problems
TL;DR: In this article, the authors remove logarithmic factors in error term estimates in asymptotic formulas for the number of solutions of a class of additive congruences modulo a prime number.
Journal ArticleDOI
Selberg's orthogonality conjecture for automorphic L-functions
Jianya Liu,Yangbo Ye +1 more
TL;DR: In this paper, the Selberg orthogonality conjecture for automorphic L -functions L ( s, π) and L( s, π'), under the Ramanujan conjecture on π and π', was proved.
Book ChapterDOI
On Dirichlet Series for Sums of Squares
TL;DR: In this article, it was shown that if f i and g i are completely multiplicative, then we have √ √ n = 1}^ √ infty (i.e.
Journal ArticleDOI
Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤ k
TL;DR: In this article, the authors established new results on sets of recurrence and van der Corput sets in Ω(k ≥ 1) for a general equidistribution result involving prime powers, which is of independent interest.
References
More filters
The gcd-sum function
TL;DR: The Dirichlet series has a compact representation in terms of the Riemann zeta function as mentioned in this paper, and asymptotic forms for values of partial sums at real values are derived, including estimates for error terms.
Journal ArticleDOI
Fermat quotients: Exponential sums, value set and primitive roots
TL;DR: In this article, Zhao et al. used the large sieve inequality to show that one can obtain a nontrivial estimate for much shorter sums starting with $N\ge p^{\epsilon}$ for any fixed > 0.
Journal ArticleDOI
On the logarithmic factor in error term estimates in certain additive congruence problems
TL;DR: In this article, the authors remove logarithmic factors in error term estimates in asymptotic formulas for the number of solutions of a class of additive congruences modulo a prime number.
Journal ArticleDOI
Selberg's orthogonality conjecture for automorphic L-functions
Jianya Liu,Yangbo Ye +1 more
TL;DR: In this paper, the Selberg orthogonality conjecture for automorphic L -functions L ( s, π) and L( s, π'), under the Ramanujan conjecture on π and π', was proved.
Book ChapterDOI
On Dirichlet Series for Sums of Squares
TL;DR: In this article, it was shown that if f i and g i are completely multiplicative, then we have √ √ n = 1}^ √ infty (i.e.