The terms in Lucas sequences divisible by their indices

The ternary Goldbach problem with arithmetic weights attached to two of the variables

The ternary Goldbach problem with primes from arithmetic progressions

The Theorem of Jentzsch--Szegő on an analytic curve. Application to the irreducibility of truncations of power series

The third moment of quadratic Dirichlet L-functions

The tower of K-theory of truncated polynomial algebras

The trace of Hecke operators on the space of classical holomorphic Siegel modular forms of genus two

The transfer operator for the Hecke triangle groups

The tree of irreducible numerical semigroups with fixed Frobenius number

The tri-pentagonal number theorem and related identities

The triangular theorem of eight and representation by quadratic polynomials

The true order of the riemann zeta--function

The twisted fourth moment of the Riemann zeta function

The twisted symmetric square $L$-function of $GL(r)$

The twisting representation of the $L$-function of a curve

The two dimensional distribution of values of $ζ(1+it)$

The u-invariant of the function fields of p-adic curves

The uniform primality conjecture for elliptic curves

The Uniform Primality Conjecture for the Twisted Fermat Cubic

The unipotent Albanese map and Selmer varieties for curves