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Pairs of diagonal quadratic forms and linear correlations among sums of two squares

  • Timothy D. Browning EMAIL logo and Ritabrata Munshi
Published/Copyright: July 10, 2015

Abstract

For suitable pairs of diagonal quadratic forms in eight variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares.

Funding source: ERC

Award Identifier / Grant number: 306457

Funding source: DST, Government of India

Award Identifier / Grant number: SwarnaJayanti Fellowship 2011–12

Received: 2013-2-11
Revised: 2013-4-3
Published Online: 2015-7-10
Published in Print: 2015-7-1

© 2015 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Notes on occupation time fluctuations of binary branching particle systems
  3. On the sum of two integral squares in certain quadratic fields
  4. A Cesàro average of Goldbach numbers
  5. Groups described by element numbers
  6. The second main theorem for entire curves into Hilbert modular surfaces
  7. L norms of holomorphic modular forms in the case of compact quotient
  8. SU(2)-Donaldson invariants of the complex projective plane
  9. Pairs of diagonal quadratic forms and linear correlations among sums of two squares
  10. The subelliptic heat kernel on the three-dimensional solvable Lie groups
  11. Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
  12. Circle-valued Morse theory for complex hyperplane arrangements
  13. Atomic Hp spaces and their duals on open subsets of ℝd
  14. Locally contractible coset spaces
  15. L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
  16. Finite time blow-up for semilinear wave equations with variable coefficients
  17. Intertwining operators of irreducible representations for exponential solvable Lie groups
  18. Artin's conjecture and systems of diagonal equations
  19. The homology of simplicial complements and the cohomology of polyhedral products
  20. Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
  21. Multilinear generalized Radon transforms and point configurations
  22. On ratios of Petersson norms for Yoshida lifts
  23. K-groups for rings of finite Cohen–Macaulay type
  24. Character degree sums of finite groups
  25. Tame Fréchet submanifolds of co-Banach type
  26. Weighted norm inequalities for Schrödinger type operators
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