3 papers
math.NT2026
Exotic and inverted Kloosterman sums over semisimple algebras
Daqing Wan, Dingxin Zhang
We introduce exotic Kloosterman sums and exotic inverted Kloosterman sums attached to non-commutative finite-dimensional semisimple algebras over a finite field , and…
math.AG2025
Hodge and Frobenius colevels of algebraic varieties
Daqing Wan, Dingxin Zhang
We provide new, improved lower bounds for the Hodge and Frobenius colevels of algebraic varieties (over or over a finite field) in all cohomological degrees. These bou…
math.AG2025
Betti number bounds for varieties and exponential sums
Daqing Wan, Dingxin Zhang
Using basic properties of perverse sheaves, we give new upper bounds for compactly supported Betti numbers for arbitrary affine varieties in defined by polynomia…