One-dimensional elementary abelian extensions have Galois scaffolding

One-Parameter Families of Unit Equations

Open conditions for infinite multiplicity eigenvalues on elliptic curves

Open Conjectures on Congruences

Open Diophantine Problems

Operations on locally free classgroups

Optimal expansions in non-integer bases

Optimal systems of fundamental S-units for LLL-reduction

Optimality of the Width-$w$ Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases

Orbital L-functions for the space of binary cubic forms

Orders of vanishing of zeros of characteristic $p$ zeta function

Ordinarization Transform of a Numerical Semigroup and Semigroups with a Large Number of Intervals

Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant

Ordinary elliptic curves of high rank over $\bar F_p(x)$ with constant j-invariant II

Orthogonal decomposition of the space of algebraic numbers and Lehmer's problem

Oscillations in Mertens Theorems and Other Finite Sums and Products

Oscillations of Hecke Eigenvalues at Primes

Other representations of the Riemann Zeta function and an additional reformulation of the Riemann Hypothesis

Overconvergence and classicality: the case of curves

Overconvergent algebraic automorphic forms