What question did this study set out to answer?

The research aims to extend classical Burgess estimates for character sums over proper generalized arithmetic progressions of rank 2.

Burgess‐type character sum estimates over generalized arithmetic progressions of rank 2

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This analysis extends Burgess estimates to character sums in prime fields, indicating novel bounds in GAPs.

The research aims to extend classical Burgess estimates for character sums over proper generalized arithmetic progressions of rank 2.
Developed sharp upper bounds for multiplicative energy of sets
Adapted techniques from Konyagin's argument
Leveraged tools from geometry of numbers
Established new upper bounds for sizes of Bohr sets
New upper bounds for character sums over rank 2 GAPs were identified
Multiplicative energy estimates were successfully extended
Production of size upper bounds for Bohr sets may hold independent significance

Alsetri et al. (2026) studied this question.

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