The variance of divisor sums in arithmetic progressions
-
Brad Rodgers
and
Kannan Soundararajan
Abstract
We study the variance of sums of the k-fold divisor function
Funding source: National Science Foundation
Award Identifier / Grant number: DMS 1500237
Funding statement: The second author is partially supported through a grant from the National Science Foundation (NSF DMS 1500237) and a Simons Investigator grant from the Simons Foundation.
Acknowledgements
We thank Adam Harper for a discussion which prompted us to think about this problem, and Régis de la Bretèche along with an anonymous referee for corrections. Some of the research for this paper was done while the first author was visiting Stanford University, which he thanks for its gracious hospitality.
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© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- The variance of divisor sums in arithmetic progressions
- Characterizing Lie groups by controlling their zero-dimensional subgroups
- CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups
- Towards a Goldberg–Shahidi pairing for classical groups
- On the non-existence of cyclic splitting fields for division algebras
- Sequential motion planning algorithms in real projective spaces: An approach to their immersion dimension
- Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
- Anharmonic solutions to the Riccati equation and elliptic modular functions
- A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp-testing condition
- Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes
- On symplectic semifield spreads of PG(5,q2), q odd
- From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
- Golodness and polyhedral products for two-dimensional simplicial complexes
Articles in the same Issue
- Frontmatter
- The variance of divisor sums in arithmetic progressions
- Characterizing Lie groups by controlling their zero-dimensional subgroups
- CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups
- Towards a Goldberg–Shahidi pairing for classical groups
- On the non-existence of cyclic splitting fields for division algebras
- Sequential motion planning algorithms in real projective spaces: An approach to their immersion dimension
- Very ampleness of the bicanonical line bundle on compact complex 2-ball quotients
- Anharmonic solutions to the Riccati equation and elliptic modular functions
- A non-homogeneous local Tb theorem for Littlewood–Paley g*λ-function with Lp-testing condition
- Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes
- On symplectic semifield spreads of PG(5,q2), q odd
- From Freudenthal’s spectral theorem to projectable hulls of unital Archimedean lattice-groups, through compactifications of minimal spectra
- Golodness and polyhedral products for two-dimensional simplicial complexes
