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On the Conditional Bounds for Siegel Zeros

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Abstract

In this paper, under a weakened version of Hardy—Littlewood Conjecture on the number of representations in Goldbach problem, we shall prove bounds for the Siegel zeros of real primitive Dirichlet characters for composite moduli.

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Acknowledgements

The author would like to thank referees for their careful reading and nice comments.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Chao Hua Jia

  2. Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Chao Hua Jia

  3. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijng, 100049, P. R. China

    Chao Hua Jia

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  1. Chao Hua Jia
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Correspondence to Chao Hua Jia.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 11771424)

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Jia, C.H. On the Conditional Bounds for Siegel Zeros. Acta. Math. Sin.-English Ser. 38, 869–876 (2022). https://doi.org/10.1007/s10114-022-0646-0

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  • DOI: https://doi.org/10.1007/s10114-022-0646-0

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