On simultaneous nonvanishing of the central $L$-values
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- by Wenzhi Luo
- Proc. Amer. Math. Soc. 145 (2017), 4227-4231
- DOI: https://doi.org/10.1090/proc/13572
- Published electronically: April 6, 2017
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Abstract:
In this note we derive a new quantitative result on the simultaneous nonvanishing of the central $L$-values twisted by quadratic characters, for pairs of holomorphic cuspidal Hecke eigenforms with large weight $2k$.References
- Erich Hecke, Mathematische Werke, 3rd ed., Vandenhoeck & Ruprecht, Göttingen, 1983 (German). With introductory material by B. Schoeneberg, C. L. Siegel and J. Nielsen. MR 749754
- Winfried Kohnen, Modular forms of half-integral weight on $\Gamma _{0}(4)$, Math. Ann. 248 (1980), no. 3, 249–266. MR 575942, DOI 10.1007/BF01420529
- Winfried Kohnen, Fourier coefficients of modular forms of half-integral weight, Math. Ann. 271 (1985), no. 2, 237–268. MR 783554, DOI 10.1007/BF01455989
- W. Kohnen and D. Zagier, Values of $L$-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), no. 2, 175–198. MR 629468, DOI 10.1007/BF01389166
- Wenzhi Luo, Nonvanishing of the central $L$-values with large weight, Adv. Math. 285 (2015), 220–234. MR 3406500, DOI 10.1016/j.aim.2015.08.009
- Jean-Loup Waldspurger, Correspondances de Shimura et quaternions, Forum Math. 3 (1991), no. 3, 219–307 (French). MR 1103429, DOI 10.1515/form.1991.3.219
- M. Young, Weyl-type hybrid subconvexity bounds for twisted L-functions and Heegner points on shrinking sets, to appear in J. Eur. Math. Society.
Bibliographic Information
- Wenzhi Luo
- Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
- MR Author ID: 260185
- Email: wluo@math.ohio-state.edu
- Received by editor(s): January 28, 2016
- Received by editor(s) in revised form: November 6, 2016
- Published electronically: April 6, 2017
- Additional Notes: This research was partially supported by NSF grant DMS-1160647
- Communicated by: Matthew A. Papanikolas
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 4227-4231
- MSC (2010): Primary 11F11, 11F37, 11F67
- DOI: https://doi.org/10.1090/proc/13572
- MathSciNet review: 3690608