3 citations · 7 across the 5 of their papers we have counts for
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On a conjecture of Wooley and lower bounds for cubic hypersurfaces
V. Vinay Kumaraswamy, Nick Rome
Let be a cubic hypersurface cut out by the vanishing of a non-degenerate rational cubic form in variables. Let denote the num…
Counting solutions to quadratic polynomials
V. Vinay Kumaraswamy
Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.
Some new results in quantitative Diophantine approximation
Anish Ghosh, V. Vinay Kumaraswamy
In this article we establish two new results on quantitative Diophantine approximation for one-parameter families of diagonal ternary indefinite forms. In the first result, we cons…
Counting integer points on quadrics with arithmetic weights
V. Vinay Kumaraswamy
Let be a diagonal, non-singular quadratic form in variables. Let be the normalised Fourier coefficients of a holomorphic Hecke form of…
On correlations between class numbers of imaginary quadratic fields
V. Vinay Kumaraswamy
Let be the class number of the imaginary quadratic field with discriminant . We establish an asymtotic formula for correlations involving and , over fu…