The factorization of over a finite field where is of first degree and L(x) is linear
The factorization of the derivative of Dickson polynomials.
The Family of Metallic Means
The Farey graph.
The Farey Series of polynomials over a finite field.
The Fekete-Szegő theorem with splitting conditions: Part I
The Fekete-Szegő theorem with splitting conditions: Part II
The Fermat equation with polynomial values as base variables.
The Fibonacci number of a grid graph and a new class of integer sequences.
The field descent and class groups of CM-fields
The field of definition for dynamical systems on
The field of moduli of abelian surfaces with complex multiplication.
The field of moduli of quaternionic multiplication on abelian varieties.
The field-of-norms functor and the Hilbert symbol for higher local fields
The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.
The fields of degree seven over rationals with a normal basis generated by a unit
The fifth taxicab number is 48988659276962496.
The finite Heine transformation and conjugate Durfee squares.
The finite subgroups of maximal arithmetic kleinian groups
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.
The first case of Fermat's last theorem.
The first moment of quadratic Dirichlet L-functions