Bounds for modular L-functions in the level aspect

Valentin Blomer[1]; Gergely Harcos; Philippe Michel

  • [1] University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)

Annales scientifiques de l'École Normale Supérieure (2007)

  • Volume: 40, Issue: 5, page 697-740
  • ISSN: 0012-9593

How to cite

top

Blomer, Valentin, Harcos, Gergely, and Michel, Philippe. "Bounds for modular L-functions in the level aspect." Annales scientifiques de l'École Normale Supérieure 40.5 (2007): 697-740. <http://eudml.org/doc/82724>.

@article{Blomer2007,
affiliation = {University of Toronto, Department of Mathematics, 100 St. George Street, Toronto M5S 3G3, Ontario, (Canada)},
author = {Blomer, Valentin, Harcos, Gergely, Michel, Philippe},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {5},
pages = {697-740},
publisher = {Elsevier},
title = {Bounds for modular L-functions in the level aspect},
url = {http://eudml.org/doc/82724},
volume = {40},
year = {2007},
}

TY - JOUR
AU - Blomer, Valentin
AU - Harcos, Gergely
AU - Michel, Philippe
TI - Bounds for modular L-functions in the level aspect
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2007
PB - Elsevier
VL - 40
IS - 5
SP - 697
EP - 740
LA - eng
UR - http://eudml.org/doc/82724
ER -

References

top
  1. [1] Blomer V., Harcos G., Hybrid bounds for twisted L-functions, J. reine angew. Math., in press. Zbl1296.11047
  2. [2] Blomer V., Harcos G., Michel P., A Burgess-like subconvex bound for twisted L-functions (with Appendix 2 by Z. Mao), Forum Math.19 (2007) 61-105. Zbl1168.11014MR2296066
  3. [3] Burgess D.A., On character sums and L-series. II, Proc. Lond. Math. Soc.13 (1963) 524-536. Zbl0123.04404MR148626
  4. [4] Bykovskiĭ V.A., A trace formula for the scalar product of Hecke series and its applications, translated in, J. Math. Sci (New York)89 (1998) 915-932. Zbl0898.11017MR1433344
  5. [5] Deshouillers J.-M., Iwaniec H., Kloosterman sums and Fourier coefficients of cusp forms, Invent. Math.70 (1982) 219-288. Zbl0502.10021MR684172
  6. [6] Duke W., Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math.92 (1988) 73-90. Zbl0628.10029MR931205
  7. [7] Duke W., Friedlander J., Iwaniec H., A quadratic divisor problem, Invent. Math.115 (1994) 209-217. Zbl0791.11049MR1258903
  8. [8] Duke W., Friedlander J., Iwaniec H., Bounds for automorphic L-functions. II, Invent. Math.115 (1994) 219-239. Zbl0812.11032MR1258904
  9. [9] Duke W., Friedlander J., Iwaniec H., Representations by the determinant and mean values of L-functions, in: Sieve Methods, Exponential Sums, and Their Applications in Number Theory, Cardiff, 1995, London Math. Soc. Lecture Note Ser., vol. 237, Cambridge Univ. Press, Cambridge, 1997, pp. 109-115. Zbl0927.11046MR1635738
  10. [10] Duke W., Friedlander J., Iwaniec H., Bounds for automorphic L-functions. III, Invent. Math.143 (2001) 221-248. Zbl1163.11325MR1835388
  11. [11] Duke W., Friedlander J., Iwaniec H., The subconvexity problem for Artin L-functions, Invent. Math.149 (2002) 489-577. Zbl1056.11072MR1923476
  12. [12] Einsiedler M., Lindenstrauss E., Michel P., Venkatesh A., Distribution of periodic torus orbits and Duke's theorem for cubic fields, submitted for publication. Zbl1248.37009
  13. [13] Friedlander J., Bounds for L-functions, in: Zürich, 1994, Proc. Int. Congr. Math., vol. II, Birkhäuser, Basel, 1995, pp. 363-373. Zbl0843.11040MR1403937
  14. [14] Gelbart S., Jacquet H., Forms on GL 2 from the analytic point of view, in: Borel A., Casselman W. (Eds.), Automorphic Forms, Representations, and L-Functions, Part 1, Proc. Sympos. Pure Math., vol. 33, 1979, pp. 213-251. Zbl0409.22013MR546600
  15. [15] Gradshteyn I.S., Ryzhik I.M., Tables of Integrals, Series, and Products, fifth ed., Academic Press, New York, 1994. Zbl0918.65002
  16. [16] Harcos G., Uniform approximate functional equation for principal L-functions, Int. Math. Res. Not. (2002) 923-932, Erratum, Int. Math. Res. Not. (2004) 659-660. Zbl0998.11026MR1902296
  17. [17] Harcos G., Michel P., The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II, Invent. Math.163 (2006) 581-655. Zbl1111.11027
  18. [18] Heath-Brown D.R., Hybrid bounds for Dirichlet L-functions. II, Quart. J. Math. Oxford Ser. (2)31 (1980) 157-167. Zbl0396.10030MR576334
  19. [19] Iwaniec H., Spectral Methods of Automorphic Forms, second ed., Graduate Studies Mathematics, vol. 53, American Mathematical Society, Providence, RI; Revista Matemática Iberoamericana, Madrid, 2002. Zbl1006.11024MR1942691
  20. [20] Iwaniec H., Kowalski E., Analytic Number Theory, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. Zbl1059.11001MR2061214
  21. [21] Iwaniec H., Sarnak P., Perspectives in the analytic theory of L-functions, Geom. Funct. Anal. (2000) 705-741, Special Volume, Part II. Zbl0996.11036MR1826269
  22. [22] Jutila M., Convolutions of Fourier coefficients of cusp forms, Publ. Inst. Math. (Beograd) (N.S.)65 (79) (1999) 31-51. Zbl1006.11019MR1717400
  23. [23] Kim H., Functoriality for the exterior square of GL 4 and the symmetric fourth of G L 2 (with Appendix 1 by D. Ramakrishnan and Appendix 2 by H. Kim and P. Sarnak), J. Amer. Math. Soc.16 (2003) 139-183. Zbl1018.11024MR1937203
  24. [24] Kowalski E., Michel P., VanderKam J., Mollification of the fourth moment of automorphic L-functions and arithmetic applications, Invent. Math.142 (2000) 95-151. Zbl1054.11026MR1784797
  25. [25] Meurman T., On the binary additive divisor problem, in: Number Theory, Turku, 1999, de Gruyter, Berlin, 2001, pp. 223-246. Zbl0967.11039MR1822012
  26. [26] Michel P., The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points, Ann. of Math.160 (2004) 185-236. Zbl1068.11033
  27. [27] Michel P., Venkatesh A., Equidistribution, L-functions and ergodic theory: on some problems of Yu. Linnik, in: Madrid, 2006, Proc. Int. Congr. Math., vol. II, Eur. Math. Soc., Zürich, 2006, pp. 421-457. Zbl1157.11019MR2275604
  28. [28] Proskurin N.V., On the general Kloosterman sums, translated in, J. Math. Sci. (New York)129 (2005) 3874-3889. Zbl1140.11340MR2023036

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.