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This study delves into the realm of chaotic dynamics derived from Dirichlet Lfunctions, drawing inspiration from Yitang Zhang's groundbreaking work onLandau Siegel zeros. The dynamic behavior reveals a profound chaos,corroborated by the calculated Lyapunov exponents and entropy, which attest tothe system's inherent unpredictability. The examination of stability furtheruncovers the instability of fixed points. Most notably, these findings unveil acompelling connection between the studied dynamics and the intricatedistribution of zeros, thereby offering indirect support for Zhang'sgroundbreaking theorem concerning Landau Siegel zeros.

Chaotic dynamics and zero distribution:Implications for Yitang Zhang's Landau Siegel zero theorem