Journal of the Ramanujan Mathematical Society

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Angular Changes of Complex Fourier Coefficients of Cusp Forms


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1 ACSA Laboratory, Department of Mathematics, Mohammed First University, Oujda, Morocco
     

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In this paper, we investigate the “angular changes” behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts of these subfamilies. These give an extension of some recent results of Kohnen and his collaborators.
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  • M. A. Amri, Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms, to appear in Ramanujan J. https://doi.org/10.1007/s11139-018-0078-8.

  • J. H. Bruinier and W. Kohnen, Sign changes of coefficients of half-integral weight modular forms, In B. Edixhoven, van der G. Gerard, and B. Moonen, editors, Modular Forms on Schiermonnikoog, Cambridge University Press (2008) 57–65.

  • P. Deligne, La conjecture de Weil I, Publ. Math., Inst. Hautes. Etud. Sci., 43 (1973) 273–307.

  • M. Fekete, Sur les s´eries de Dirichlet, Comptes rendus hebdomadaires des s´eances de l’Acad´emie des sciences, 150 (1910) 1033–1036.

  • T. A. Hulse, C. I. Kuan, D. Lowry-Duda and A. Walker, Sign changes of coefficients and sums of coefficients of L-functions, J. Number Theory, 177 (2017) 112–135.

  • I. Inam and G. Wiese, Equidistribution of signs for modular eigenforms of half integral weight, Arch. Math., 101 (2013) 331–339.

  • M. Knopp, W. Kohnen and W. Pribitkin, On the signs of Fourier coefficients of cusp forms, Ramanujan J., 7 (2003) 269–277.

  • W. Kohnen, A short note on Fourier coefficients of half-integral weight modular forms, Int. J. of Number Theory, 6 (2010) 1255–1259.

  • W. Kohnen and Y. Martin, Sign changes of Fourier coefficients of cusp forms supported on prime power indices, Int. J. of Number Theory, 10 (2014) 1921–1927.

  • B. N. Maurizi, Extending Landau’s Theorem on Dirichlet series with non-negative coefficients, Missouri J. Math. Sci., 23 (2011) 105–122.

  • M. Ram Murty, Oscillations of Fourier coefficients of modular forms, Math. Ann. (1983) 431–446.

  • S. Niwa, Modular forms of half-integral weight and the integral of certain theta-functions, Nagoya Math. J., 56 (1975) 147–161.

  • G. Shimura, On modular forms of half-integral weight, Ann. of Math., 97 (1973) 440–481.


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  • Angular Changes of Complex Fourier Coefficients of Cusp Forms

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Authors

Mohammed Amin Amri
ACSA Laboratory, Department of Mathematics, Mohammed First University, Oujda, Morocco

Abstract


In this paper, we investigate the “angular changes” behavior of some subfamilies of Fourier coefficients of both integral and half-integral weight holomorphic cusp forms, thus one gets information about signs of the real an imaginary parts of these subfamilies. These give an extension of some recent results of Kohnen and his collaborators.

References