On the restricted divisor function in arithmetic progressions
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Publication:664905
DOI10.4171/RMI/675zbMath1323.11073arXiv1003.5347OpenAlexW2031906135MaRDI QIDQ664905
Publication date: 3 March 2012
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1003.5347
asymptotic estimatecharacter sumsdivisor functionaverage resultscongruence solutionsrestricted divisor function
Asymptotic results on arithmetic functions (11N37) Distribution of integers with specified multiplicative constraints (11N25) Rate of growth of arithmetic functions (11N56)
Related Items (4)
The variance of a restricted sum-of-squares function over short intervals in \(\mathbb{F}_q [t\)] ⋮ Modular hyperbolas ⋮ On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics ⋮ Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions
Cites Work
- The equation \(x_1x_2=x_3x_4+\lambda \) in fields of prime order and applications
- Incomplete Kloosterman sums and a divisor problem. Appendix: On some exponential sums by Bryan J. Birch and Enrico Bombieri
- The congruence \(x_ 1x_ 2\equiv x_ 3x_ 4\pmod p\), the equation \(x_ 1x_ 2=x_ 3x_ 4\), and mean values of character sums
- The congruence \(x_1 x_2 \equiv x_3 x_4\) and mean values of character sums
- Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average
- Sur le problème des diviseurs de Titchmarsh.
- THE AVERAGE VALUE OF DIVISOR SUMS IN ARITHMETIC PROGRESSIONS
- Pair correlation for fractional parts of αn2
- Divisor Problems and the Pair Correlation for the Fractional Parts of n2
- The divisor problem for arithmetic progressions
- The distribution of spacings between the fractional parts of \(n^2\alpha\)
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