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