A new zero-density estimate for Dirichlet L-functions with exponent 7/3, improving Huxley's 12/5, is proven by extending the Guth-Maynard large value method to character-twisted Dirichlet polynomials.
Bourgain, Remarks on Montgomery’s conjectures on Dirichlet series, Geometric Aspects of Functional Analysis (1989–1990), Springer Lecture Notes in Mathematics 1469 (1991), 153–165
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Large Value Estimates for Dirichlet Polynomials with Characters and Zero Density of Dirichlet $L$-Functions
A new zero-density estimate for Dirichlet L-functions with exponent 7/3, improving Huxley's 12/5, is proven by extending the Guth-Maynard large value method to character-twisted Dirichlet polynomials.