Skip to main content Accessibility help
×
Home

QUANTITATIVE ESTIMATES FOR SIMPLE ZEROS OF $L$ -FUNCTIONS

  • Andrew R. Booker (a1), Micah B. Milinovich (a2) and Nathan Ng (a3)

Abstract

We generalize a method of Conrey and Ghosh [Simple zeros of the Ramanujan $\unicode[STIX]{x1D70F}$ -Dirichlet series. Invent. Math. 94(2) (1988), 403–419] to prove quantitative estimates for simple zeros of modular form $L$ -functions of arbitrary conductor.

Copyright

Footnotes

Hide All

Research of the first author was supported by EPSRC Grant EP/K034383/1. Research of the second author was supported by the NSA Young Investigator Grants H98230-15-1-0231 and H98230-16-1-0311. Research of the third author was supported by NSERC Discovery Grant (RGPIN-2015-05972). No data were created in the course of this study.

Footnotes

References

Hide All
1. Booker, A. R., Simple zeros of degree 2 L-functions. J. Eur. Math. Soc. (JEMS) 18(4) 2016, 813823; MR 3474457.
2. Booker, A. R. and Krishnamurthy, M., A strengthening of the GL(2) converse theorem. Compos. Math. 147(3) 2011, 669715; MR 2801397.
3. Booker, A. R., Milinovich, M. B. and Ng, N., Subconvexity for modular form L-functions in the t aspect. Adv. Math. 341 2019, 299335; MR 3872849.
4. Coleman, M. D., A zero-free region for the Hecke L-functions. Mathematika 37(2) 1990, 287304; MR 1099777.
5. Conrey, J. B. and Ghosh, A., Simple zeros of the Ramanujan 𝜏-Dirichlet series. Invent. Math. 94(2) 1988, 403419; MR 958837 (89k:11078).
6. Iwaniec, H. and Kowalski, E., Analytic Number Theory (Colloquium Publications 53 ), American Mathematical Society (Providence, RI, 2004); MR 2061214.
7. Jacquet, H. and Shalika, J. A., A non-vanishing theorem for zeta functions of GL n . Invent. Math. 38(1) 1976/77, 116; MR 0432596 (55 #5583).
8. Kowalski, E., Michel, P. and VanderKam, J., Rankin–Selberg L-functions in the level aspect. Duke Math. J. 114(1) 2002, 123191; MR 1915038.
9. Milinovich, M. B. and Ng, N., Simple zeros of modular L-functions. Proc. Lond. Math. Soc. (3) 109(6) 2014, 14651506; MR 3293156.
10. Munshi, R., Sub-Weyl bounds for $\text{GL}(2)\;L$ -functions. Preprint, 2018, arXiv:1806.07352.
11. Weil, A., Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen. Math. Ann. 168 1967, 149156; MR 0207658 (34 #7473).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

MSC classification

QUANTITATIVE ESTIMATES FOR SIMPLE ZEROS OF $L$ -FUNCTIONS

  • Andrew R. Booker (a1), Micah B. Milinovich (a2) and Nathan Ng (a3)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed