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

Timothy D. Browning 1  and Ritabrata Munshi 2
  • 1 School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom
  • 2 Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Colaba, Mumbai 400005, India


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.

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