On the average value of divisor sums in arithmetic progressions

On the average value of divisor sums in arithmetic progressions

We consider very short sums of the divisor function in arithmetic progressions prime to a fixed modulus and show that ``on average'' these sums are close to the expected value. We also give applications of our result to sums of the divisor function twisted with characters (both additive a...

Bibliografske podrobnosti
Main Authors:	Heath-Brown, D, Banks, W, Shparlinski, I
Format:	Journal article
Izdano:	2005

Podobne knjige/članki

Averages of ratios of the Riemann zeta-function and correlations of divisor sums
od: Conrey, B, et al.
Izdano: (2017)

Variance of sums in arithmetic progressions of divisor functions associated with higher degree 𝐿-Functions in 𝔽q[𝑡]
od: Roditty-Gershon, E, et al.
Izdano: (2019)

On the sum of positive divisors functions
od: Erban, R, et al.
Izdano: (2021)

Equal sums in random sets and the concentration of divisors
od: Ford, K, et al.
Izdano: (2023)

Moments of zeta and correlations of divisor-sums: V
od: Conrey, B, et al.
Izdano: (2018)

Sums of divisor functions in Fq[t] and matrix integrals
od: Keating, J, et al.
Izdano: (2017)

The distribution and moments of the error term in the Dirichlet divisor problem
od: Heath-Brown, D
Izdano: (1992)

Rational Divisors in Rational Divisor Classes.
od: Bruin, N, et al.
Izdano: (2004)

Rational divisors in rational divisor classes
od: Bruin, N, et al.
Izdano: (2004)

Siegel zeros and the least prime in an arithmetic progression
od: Heath-Brown, D
Izdano: (1990)

A mean value estimate for real character sums
od: Heath-Brown, D
Izdano: (1995)

Divisor theory in module categories /
od: 362192 Vasconcelos, W.
Izdano: (1974)

Zero-free regions for Dirichlet $L$-functions, and the least prime in an arithmetic progression
od: Heath-Brown, D
Izdano: (1992)

Variance of arithmetic sums and L-functions in Fq[t]
od: Hall, C, et al.
Izdano: (2019)

Mean values of arithmetic functions in short intervals and in arithmetic progressions in the large-degree limit
od: Gorodetsky, O
Izdano: (2020)

Superpotentials from singular divisors
od: Gendler, Naomi, et al.
Izdano: (2022)

On the variety of special divisors and moduli,
od: Lax, R. F.
Izdano: (2022)

Metric theory of Weyl sums
od: Chen, C, et al.
Izdano: (2022)

Topics in arithmetical functions : asymptotic formulae for sums of reciprocals of arithmetical functions and related results /
od: 365490 Dekoninck, J. M., et al.
Izdano: (1980)

A new 𝘬th derivative estimate for exponential sums via Vinogradov’s mean value
od: Heath-Brown, D
Izdano: (2017)

Squarefree polynomials and möbius values in short intervals and arithmetic progressions
od: Keating, JP, et al.
Izdano: (2016)

Numerical properties of pseudo-effective divisors
od: Lehmann, Brian (Brian Todd)
Izdano: (2010)

Density of non-residues in Burgess-type intervals and applications
od: Heath-Brown, D, et al.
Izdano: (2008)

Density of non-residues in Burgess-type intervals and applications
od: Banks, W, et al.
Izdano: (2008)

An estimate for Heilbronn's exponential sum
od: Heath-Brown, D
Izdano: (1996)

Bounds for the Cubic Weyl Sum
od: Heath-Brown, D
Izdano: (2010)

New bounds for Gauss sums derived from kth powers, and for Heilbronn's exponential sum
od: Heath-Brown, D, et al.
Izdano: (2000)

Equal Sums of three powers
od: Browning, T, et al.
Izdano: (2004)

Equal sums of three powers
od: Browning, T, et al.
Izdano: (2004)

Every sum of cubes in F2[t] is a strict sum of 6 cubes.
od: Gallardo, L, et al.
Izdano: (2007)

Long arithmetic progressions of primes
od: Green, B
Izdano: (2005)

Bounds for the cubic Weyl sum
od: Heath-Brown, DR
Izdano: (2010)

Heilbronn's exponential sum and transcendence theory
od: Heath-Brown, D
Izdano: (2002)

Heilbronn's exponential sum and transcendence theory
od: Heath-Brown, D
Izdano: (2002)

Kummer's conjecture for cubic Gauss sums
od: Heath-Brown, D
Izdano: (2000)

Kummer's conjecture for cubic Gauss sums
od: Heath-Brown, D
Izdano: (2000)

Exotic matter on singular divisors in F-theory
od: Klevers, Denis, et al.
Izdano: (2018)

New bounds for Gauss sums derived from $k$-th powers, and for Heilbronn's exponential sum
od: Heath-Brown, D, et al.
Izdano: (2000)

Simultaneous equal sums of three powers
od: Heath-Brown, D, et al.
Izdano: (2007)

The average rank of elliptic curves
od: Heath-Brown, D
Izdano: (2004)