Archiv der Mathematik

, Volume 111, Issue 3, pp 257–266 | Cite as

Simultaneous sign change and equidistribution of signs of Fourier coefficients of two cusp forms

  • Mohammed Amin Amri


We study the simultaneous sign change of Fourier coefficients of a pair of distinct normalized newforms of integral weight supported on primes power indices, we also prove some equidistribution results. Finally, we consider an analogous question for Fourier coefficients of a pair of half-integral weight Hecke eigenforms.


Simultaneous sign changes Fourier coefficients Sato–Tate conjecture. 

Mathematics Subject Classification

Primary 11F03 Secondary 11F30 11F37 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Amri, M.A.: Angular changes of complex Fourier coefficients of cusp forms. arXiv:1704.00982
  2. 2.
    Amri, M.A.: Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms. arXiv:1710.06211
  3. 3.
    Amri, M.A., Ziane, M.: A note on the extended Bruinier–Kohnen conjecture. arXiv:1711.02431
  4. 4.
    Bruinier, J.H., Kohnen, W.: Sign changes of coefficients of half integral weight modular forms. In: Edixhoven, B., van der Gerard, G., Moonen, B. (eds.) Modular Forms on Schiermonnikoog, pp. 57–65. Cambridge University Press, Cambridge (2008)CrossRefGoogle Scholar
  5. 5.
    Fung, K.C., Kane, B.: On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring. Math. Comput. 87, 501–514 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gun, S., Kohnen, W., Rath, P.: Simultaneous sign change of Fourier-coefficients of two cusp forms. Arch. Math. 105, 413–424 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Inam, I., Wiese, G.: Equidistribution of signs for modular eigenforms of half integral weight. Arch. Math. 101, 331–339 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kohnen, W.: A short note on Fourier coefficients of half-integral weight modular forms. Int. J. Number Theory 6, 1255–1259 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kohnen, W., Sengupta, J.: Signs of Fourier coefficients of two cusp forms of different weights. Proc. Amer. Math. Soc. 137, 3563–3567 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Kohnen, W., Lau, Y.K., Wu, J.: Fourier coefficients of cusp forms of half-integral weight. Math. Z. 273, 29–41 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. Wiley, New York (1974)zbMATHGoogle Scholar
  12. 12.
    Kumar, N.: A variant of multiplicity one theorems for half-integral weight modular forms. arXiv:1709.04674
  13. 13.
    Lau, Yk, Royer, E., Wu, J.: Sign of Fourier coefficients of modular forms of half-integral weight. Mathematika 62, 866–883 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Meher, J., Shankhadhar, K.D., Viswanadham, G.K.: On the coefficients of symmetric power \({L}\)-functions. Int. J. Number Theory 14, 813–824 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Niwa, S.: Modular forms of half integral weight and the integral of certain theta-functions. Nagoya Math. J. 56, 147–161 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Shimura, G.: On modular forms of half-integral weight. Ann. Math. 97, 440–481 (1973).
  17. 17.
    Siegel, C.L.: Berechnung von Zetafunktionen an ganzzahligen Stellen. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, 87–102 (1969)Google Scholar
  18. 18.
    Wong, P.J.: On the chebotarev-Sato-Tate phenomenon. Preprint (2017).

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ACSA Laboratory, Department of Mathematics, Faculty of SciencesMohammed First UniversityOujdaMorocco

Personalised recommendations