Some Problems Related to Sun Zhiwei's Conjectures

Xingxing LÜ, Wenpeng Zhang

Acta Mathematica Sinica, Chinese Series ›› 2025, Vol. 68 ›› Issue (1) : 126-134.

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Acta Mathematica Sinica, Chinese Series ›› 2025, Vol. 68 ›› Issue (1) : 126-134. DOI: 10.12386/A20220007

Some Problems Related to Sun Zhiwei's Conjectures

  • Xingxing LÜ1, Wenpeng Zhang2
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Abstract

In this paper, we study the computational problems of one kind congruent equation modulo p, and give some exact computational formulae for them.

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Congruence equation / analytic methods / trigonometrical sums / computational formula

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Xingxing Lü , Wenpeng Zhang. Some Problems Related to Sun Zhiwei's Conjectures. Acta Mathematica Sinica, Chinese Series, 2025, 68(1): 126-134 https://doi.org/10.12386/A20220007

References

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[2] Burgess D. A., On Dirichlet characters of polynomials, Proc. London Math. Soc., 1963, 13: 537-548.
[3] Ireland K., Rosen M., A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982.
[4] Iwaniec H., Kowalski E., Analytic Number Theory, Higher Education Press, Beijing, 2019(in Chinese).
[5] Sun Z. W., New Conjectures in Number Theory and Combinatorics, Harbin Institute of Technology Press, Harbin, 2021.
[6] Weil A., On some exponential sums, Proc. Nat. Acad. Sci. U.S.A., 1948, 34: 203-210.
[7] Zhang W. P., Li H. L., Elementary Number Theory, Shaanxi Normal University Press, Xi’an, 2013(in Chinese).
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