5 problems

A period is a number admitting an integral representation whose functions and domains of integration are algebraic with coefficients in $\bar{\mathbb{Q}}$. The relevant transformat…

Let $a,b\in\mathbb R$ and let $p\in\mathbb R$ be an exponent for which the integral and the displayed powers are defined. Power-function integration conjecture. The integration for…

The exponential addition-law conjecture. The relationship

For each positive real number $a$, consider the curve through the points $(n,a^n)$ with integer coordinates and its tangent line at $(0,1)$. The tangent-slope conjecture. The slope…

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…