Abstract
We prove a non-vanishing result in weight aspect for the product of two Fourier coefficients of a Hecke eigenform of half-integral weight.
Similar content being viewed by others
References
Das, S., Kohnen, W.: Non-vanishing of Koecher–Maass series attached to Siegel cusp forms. Adv. Math. 281, 624–669 (2015)
Freitag, E.: Siegelsche Modulformen, Grundl. Math. Wiss., vol. 254. Springer, Berlin (1983)
Gross, B., Kohnen, W., Zagier, D.: Heegner points and derivatives of \(L\)-series. II. Math. Ann. 278, 497–562 (1987)
Kohnen, W.: Modular forms of half-integral weight on \(\Gamma _0(4)\). Math. Ann. 248, 249–288 (1980)
Kohnen, W.: Fourier coeficients of modular forms of half-integral weight. Math. Ann. 271, 237–268 (1985)
Kohnen, W.: Non-vanishing of Hecke \(L\)-functions associated to cusp forms inside the critical strip. J. Number Theory 67(2), 182–189 (1997)
Kohnen, W., Raji, W.: Non-vanishing of \(L\)-functions associated to cusp forms of half-integral weight in the plus space. Res. Number Theory 3, 6 (2017)
Kohnen, W., Zagier, D.: Values of \(L\)-series of modular forms at the center of the critical strip. Invent. Math. 64, 175–198 (1981)
Kohnen, W., Zagier, D.: Modular forms with rational periods. In: Rankin, R.A. (ed.) Modular Forms, pp. 197–249. Ellis Horwood Limited Publishers, Chichester (1984)
Raghuram, A.: Non-vanishing of \(L\)-functions of cusp forms inside the critical strip. In: Number Theory, Ramanujan Math. Soc. Lect. Notes Ser. 1, pp. 97–105. Ramanujan Math. Soc., Mysore (2005)
Ramakrishnan, B., Shankhadhar, D.: Non-vanishing of \(L\)-functions associated to cusp forms of half-integral weight. In: Automorphic Forms, Springer Proceedings in Mathematics and Statistics, vol. 115, pp. 223–231. Springer, Cham (2014)
Waldspurger, J.L.: Sur les coefficients de Fourier des formes modulaires de poids demi-entier. J. Math. Pures Appl. 60, 375–484 (1981)
Zagier, D.: Modular forms associated to real quadratic fields. Invent. Math. 30, 1–46 (1975)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Jens Funke.
Rights and permissions
About this article
Cite this article
Kohnen, W. Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight. Abh. Math. Semin. Univ. Hambg. 88, 371–376 (2018). https://doi.org/10.1007/s12188-018-0194-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12188-018-0194-9