Startseite Mathematik Bounds for GL3L-functions in depth aspect
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Bounds for GL3L-functions in depth aspect

  • Qingfeng Sun EMAIL logo und Rui Zhao
Veröffentlicht/Copyright: 17. Oktober 2018
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 31 Heft 2

Abstract

Let f be a Hecke–Maass cusp form for SL3⁢(ℤ) and χ a primitive Dirichlet character of prime power conductor 𝔮=pκ, with p prime. We prove the subconvexity bound

L⁢(12,π⊗χ)≪p,π,ε𝔮3/4-3/40+ε

for any ε>0, where the dependence of the implied constant on p is explicit and polynomial.

Keywords: Subconvexity; depth aspect
MSC 2010: 11F66; 11F67; 11M41

Communicated by Freydoon Shahidi

Funding source: Natural Science Foundation of China

Award Identifier / Grant number: 11871306

Funding source: Natural Science Foundation of Shandong Province

Award Identifier / Grant number: ZR2016AQ15

Funding source: Ministry of Education of the People’s Republic of China

Award Identifier / Grant number: IRT16R43

Funding statement: The first author is supported by the National Natural Science Foundation of China (Grant No. 11871306), Natural Science Foundation of Shandong Province (Grant No. ZR2016AQ15) and PCSIRT (Grant No. IRT16R43).

Acknowledgements

The authors would like to express heartfelt thanks to the referees for their important and useful comments.

References

[1] V. Blomer, Subconvexity for twisted L-functions on GL⁢(3), Amer. J. Math. 134 (2012), no. 5, 1385–1421. 10.1353/ajm.2012.0032Suche in Google Scholar

[2] V. Blomer and D. Milićević, p-adic analytic twists and strong subconvexity, Ann. Sci. Éc. Norm. Supér. (4) 48 (2015), no. 3, 561–605. 10.24033/asens.2252Suche in Google Scholar

[3] J. B. Conrey and H. Iwaniec, The cubic moment of central values of automorphic L-functions, Ann. of Math. (2) 151 (2000), no. 3, 1175–1216. 10.2307/121132Suche in Google Scholar

[4] D. Goldfeld and X. Li, Voronoi formulas on GL⁢(n), Int. Math. Res. Not. IMRN 2006 (2006), Article ID 86295. 10.1155/IMRN/2006/86295Suche in Google Scholar

[5] A. Good, The square mean of Dirichlet series associated with cusp forms, Mathematika 29 (1982), no. 2, 278–295. 10.1112/S0025579300012377Suche in Google Scholar

[6] R. Holowinsky and P. D. Nelson, Subconvex bounds on GL3 via degeneration to frequency zero, Math. Ann. 372 (2018), no. 1–2, 299–319. 10.1007/s00208-018-1711-ySuche in Google Scholar

[7] H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ. 53, American Mathematical Society, Providence, 2004. 10.1090/coll/053Suche in Google Scholar

[8] M. Jutila, Lectures on a Method in the Theory of Exponential Sums, Tata Inst. Fundam. Res. Lectures Math. Phys. 80, Springer, Berlin, 1987. Suche in Google Scholar

[9] D. D. Letang, Subconvexity Bounds for Automorphic L-functions on GL2, ProQuest LLC, Ann Arbor, 2009; Thesis (Ph.D.)–University of Minnesota. Suche in Google Scholar

[10] X. Li, Bounds for GL⁢(3)×GL⁢(2)L-functions and GL⁢(3)L-functions, Ann. of Math. (2) 173 (2011), no. 1, 301–336. 10.4007/annals.2011.173.1.8Suche in Google Scholar

[11] T. Meurman, On the order of the Maass L-function on the critical line, Number Theory. Vol. I (Budapest 1987), Colloq. Math. Soc. János Bolyai 51, North-Holland, Amsterdam (1990), 325–354. Suche in Google Scholar

[12] D. Milićević, Sub-Weyl subconvexity for Dirichlet L-functions to prime power moduli, Compos. Math. 152 (2016), no. 4, 825–875. 10.1112/S0010437X15007381Suche in Google Scholar

[13] S. D. Miller and W. Schmid, Automorphic distributions, L-functions, and Voronoi summation for GL⁢(3), Ann. of Math. (2) 164 (2006), no. 2, 423–488. 10.4007/annals.2006.164.423Suche in Google Scholar

[14] G. Molteni, Upper and lower bounds at s=1 for certain Dirichlet series with Euler product, Duke Math. J. 111 (2002), no. 1, 133–158. 10.1215/S0012-7094-02-11114-4Suche in Google Scholar

[15] R. Munshi, Bounds for twisted symmetric square L-functions—III, Adv. Math. 235 (2013), 74–91. 10.1016/j.aim.2012.11.010Suche in Google Scholar

[16] R. Munshi, The circle method and bounds for L-functions. II: Subconvexity for twists of GL⁢(3)L-functions, Amer. J. Math. 137 (2015), no. 3, 791–812. 10.1353/ajm.2015.0018Suche in Google Scholar

[17] R. Munshi, The circle method and bounds for L-functions. III: t-aspect subconvexity for GL⁢(3)L-functions, J. Amer. Math. Soc. 28 (2015), no. 4, 913–938. 10.1090/jams/843Suche in Google Scholar

[18] R. Munshi, The circle method and bounds for L-functions. IV: Subconvexity for twists of GL⁢(3)L-functions, Ann. of Math. (2) 182 (2015), no. 2, 617–672. 10.4007/annals.2015.182.2.6Suche in Google Scholar

[19] R. Munshi, Twists of GL⁢(3)L-functions, preprint (2016), https://arxiv.org/abs/1604.08000. Suche in Google Scholar

[20] H. Weyl, Zur Abschätzung von ζ⁢(1+i⁢t), Math. Z. 10 (1921), 88–101. 10.1007/BF02102307Suche in Google Scholar

Received: 2018-04-11
Revised: 2018-08-28
Published Online: 2018-10-17
Published in Print: 2019-03-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
  3. Infinite families of equivariantly formal toric orbifolds
  4. Bounds for GL3L-functions in depth aspect
  5. Nonlinear Dirichlet problems with unilateral growth on the reaction
  6. K-invariant cusp forms for reductive symmetric spaces of split rank one
  7. Cellularity in quotient spaces of topological groups
  8. Shifted convolution sums for higher rank groups
  9. Dimension quotients, Fox subgroups and limits of functors
  10. Large sums of Hecke eigenvalues of holomorphic cusp forms
  11. K-theory classification of graded ultramatricial algebras with involution
  12. Regularity of symbolic powers and arboricity of matroids
  13. On some problems concerning symmetrization operators
  14. An Erdős–Ko–Rado result for sets of pairwise non-opposite lines in finite classical polar spaces
  15. Rankin–Selberg gamma factors of level zero representations of GLn
  16. Sobolev’s inequality for double phase functionals with variable exponents
  17. Independence of Artin L-functions
  18. Oscillatory singular integral operators with Hölder class kernels on Hardy spaces
https://doi.org/10.1515/forum-2018-0080
Schlagwörter für diesen Artikel
Subconvexity; depth aspect

Artikel in diesem Heft

  1. Frontmatter
  2. Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups
  3. Infinite families of equivariantly formal toric orbifolds
  4. Bounds for GL3L-functions in depth aspect
  5. Nonlinear Dirichlet problems with unilateral growth on the reaction
  6. K-invariant cusp forms for reductive symmetric spaces of split rank one
  7. Cellularity in quotient spaces of topological groups
  8. Shifted convolution sums for higher rank groups
  9. Dimension quotients, Fox subgroups and limits of functors
  10. Large sums of Hecke eigenvalues of holomorphic cusp forms
  11. K-theory classification of graded ultramatricial algebras with involution
  12. Regularity of symbolic powers and arboricity of matroids
  13. On some problems concerning symmetrization operators
  14. An Erdős–Ko–Rado result for sets of pairwise non-opposite lines in finite classical polar spaces
  15. Rankin–Selberg gamma factors of level zero representations of GLn
  16. Sobolev’s inequality for double phase functionals with variable exponents
  17. Independence of Artin L-functions
  18. Oscillatory singular integral operators with Hölder class kernels on Hardy spaces
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2026 De Gruyter Brill
Heruntergeladen am 30.1.2026 von https://www.degruyterbrill.com/document/doi/10.1515/forum-2018-0080/html?lang=de
Button zum nach oben scrollen