Universal torsors over Del Pezzo surfaces and rational points

Unobstructed modular deformation problems

Unramified alternating extensions of quadratic fields

Unramified extensions and geometric $\mathbb{Z}_p$-extensions of global function fields

Upper bound on the number of systems of Hecke eigenvalues for Siegel modular forms (mod p)

Upper Bounds for the Davenport Constant

Upper bounds for the growth of Mordell-Weil ranks in pro-p towers of Jacobians

Upper bounds for the moments of zeta prime rho

Upper Bounds for the Number of Number Fields with Alternating Galois Group

Upper bounds for the number of solutions to quartic Thue equations

Upper bounds for the order of an additive basis obtained by removing a finite subset of a given basis

Upper bounds for |L(1,chi)|

Upper bounds on L-functions at the edge of the critical strip

Upper bounds on the solutions to $n = p+m^2$

Using elliptic curves of rank one towards the undecidability of Hilbert's Tenth Problem over rings of algebraic integers

Using hyperelliptic curves to find positive polynomials that are not a sum of three squares in R(x, y)

Using Indices of Points on an Elliptic Curve to Construct A Diophantine Model of $\Z$ and Define $\Z$ Using One Universal Quantifier in Very Large Subrings of Number Fields, Including $\Q$

Using Lucas Sequences to Generalize a Theorem of Sierpiński

Using the smoothness of p-1 for computing roots modulo p

Vacca-type series for values of the generalized-Euler-constant function and its derivative