3 problems

Let $f_b(x):=\frac{1}{1-bx+x^2}$, and let $\beta^+=\frac{3+\sqrt{13}}{4}$. Monotonicity conjecture. 1. $L_n(f_b)$ is neither increasing nor decreasing for all…

Let $P$ be an integer polyhedron and let $g(x)$ be a smooth function. Consider the weighted Riemann sums associated with $P$ and $g$, and the Fourier transform of $g\chi_P$. Fourie…

Let a continuous curve be given, and consider a uniform Riemann sum for it together with a Riemann sum whose limit is infinite. Asymptotic equivalence conjecture. A uniform Riemann…