Counterexamples to a Conjecture of Ahmadi and Shparlinski

2020/03/11 by Dupuy, Taylor, Kedlaya, Kiran, Roe, David +1
#11G10 (Primary) 14K15 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.05368

Abstract

Ahmadi-Shparlinski conjectured that every ordinary, geometrically simple Jacobian over a finite field has maximal angle rank. Using the L-Functions and Modular Forms Database, we provide two counterexamples to this conjecture in dimension 4.

Related

• Angle ranks of abelian varieties
• Ranks of Jacobians in towers of function fields
• Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields
• Upper bounds for the growth of Mordell-Weil ranks in pro-p towers of Jacobians
• Explicit upper bound for the rank of J₀(q)