Fourier analysis and nonlinear progressions of integers

Abstract: Fourier analysis has proved a fundamental tool in analytic and combinatorial number theory, usually in the guise of the Hardy-Littlewood circle method. When applicable, this method allows one to asymptotically estimate the number of solutions to a given Diophantine equation with variables constrained to a given finite set of integers. I will discuss recent work, obtained jointly with Sarah Peluse, which adapts the circle method to count the configuration $x, x+y, x+y^2$ in a quantitatively effective manner.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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