Advertisement

Archiv der Mathematik

, Volume 96, Issue 3, pp 235–245 | Cite as

On a hybrid bound for twisted L-values

  • Ritabrata Munshi
Article

Abstract

Let f S k (M, ψ) be a newform, and let χ be a primitive character of conductor q. We express \({L(\frac{1}{2}+it,f\otimes\chi)}\) as a short combination of bilinear forms involving Kloosterman fractions. Using this we establish the convexity breaking bound \({L\left(\tfrac{1}{2}+it,f\otimes\chi\right)\ll_{f,\varepsilon} [q(1+|t|)]^{\frac{1}{2}-\frac{1}{118}+\varepsilon}}\) for any ε > 0.

Mathematics Subject Classification (2010)

Primary 11F66 Secondary 11M41 

Keywords

L-functions Subconvexity Hybrid bound 

References

  1. 1.
    Blomer V., Blomer V.: L-functions on the critical line. Manuscr Math. 117, 111–133 (2005)CrossRefMATHGoogle Scholar
  2. 2.
    Blomer V., Harcos G.: Hybrid bounds for twisted L-functions. J. Reine Angew. Math. 621, 53–79 (2008)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Bykovskii V.A..: A trace formula for the scalar product of Hecke series and its applications. J. Math. Sci. (New York) 89, 915–932 (1998)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Duke W., Friedlander J., Iwaniec H.: Bilinear forms with Kloosterman fractions. Invent. Math. 128, 23–43 (1997)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Duke W., Friedlander J., Iwaniec H.: The subconvexity problem for Artin L-functions. Invent. Math. 149, 489–577 (2002)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Heath-Brown D.R.: Hybrid bounds for Dirichlet L-functions II, Quart. J. Math. Oxford Ser 2(31), 157–167 (1980)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Iwaniec H., Kowalski E.: Analytic Number Theory, Amer. Math. Soc. Coll. Publ. 53. American Mathematical Society, Providence, RI (2004)Google Scholar
  8. 8.
    M. Jutila and Y. Motohashi, Uniform bounds for Hecke L-functions, Acta Math. 195 (2005), 61–115.CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Michel P., Venkatesh A.: The subconvexity problem for GL2, Publ. Math. Inst. Hautes Études Sci. 111, 171–271 (2010)MathSciNetGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia

Personalised recommendations