INVARIANTS OF GLn(Fq) IN POLYNOMIALS MOD FROBENIUS POWERS

Invariants of GLn(Fq) in polynomials modulo Frobenius powers

GLn(Fq) in polynomials modulo Frobenius powers

EXPLICIT REALIZATION OF THE DICKSON GROUPS G2(q) AS GALOIS GROUPS

In this paper we are concerned with the construction of polynomials whose Galois groups are the exceptional simple Chevalley groups G2(q), q a prime power, first discovered by Dickson; see Theorems 4.1 and 4.3. It was shown by Nori [7] that all semisimple simply-connected linear algebraic groups over Fq do occur as Galois groups of regular extension of regular function fields over Fq, but his p...

HYPERGEOMETRIC FUNCTIONS OVER Fq AND TRACES OF FROBENIUS FOR ELLIPTIC CURVES

We present explicit relations between the traces of Frobenius endomorphisms of certain families of elliptic curves and special values of 2F1hypergeometric functions over Fq for q ≡ 1(mod 6) and q ≡ 1(mod 4).

Pk-torsion of Genus Two Curves over 𝔽pm

We determine the isogeny classes of abelian surfaces over Fq whose group of Fq-rational points has order divisible by q . We also solve the same problem for Jacobians of genus-2 curves. In a recent paper [4], Ravnshøj proved: if C is a genus-2 curve over a prime field Fp, and if one assumes that the endomorphism ring of the Jacobian J of C is the ring of integers in a primitive quartic CM-field...