Skip to main content
SpringerLink
Log in

Special values of Hecke L-functions of modular forms of half-integral weight and cohomology

  • Research
  • Published:
Research in the Mathematical Sciences Aims and scope Submit manuscript

Abstract

We start developing a cohomology theory in the case of half-integral weight with an attempt to focus again on the connection to special values of L-functions at half-integral and integral points inside the critical strip.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abramowitz, M., Stegun, I.: Handbook of Mathematical Functions. Dover, New York (1965)

    MATH  Google Scholar 

  2. Bringmann, K., Rolen, L.: Half-integral weight Eichler integrals and quantum modular forms. Ramanujan J. (2018, Accepted)

  3. Bruggeman, R., Choie, Y.J., Diamantis, N.: Holomorphic automorphic forms and cohomology. arXiv: 1404.6718 (2017)

  4. Chen, B., Yuan, P.Z.: Congruence subgroups of Hecke groups. Acta Math. Sin. Engl. Ser. 25(6), 931–944 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Choi, D., Lim, S., Rhoades, R.: Mock modular forms and Quantum modular forms. Proc. Am. Math. Soc. 144, 2337–2349 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Choie, Y.J.: Hecke operators on rational period functions on the Hecke groups. Results Math. 25, 40–49 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cohen, H.: Sums involving the values at negative integers of \(L\)-functions of quadratic characters. Math. Ann. 217, 271–285 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  8. Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Table of Integral Transforms, vol. 1. McGraw-Hill, New York (1954)

    MATH  Google Scholar 

  9. Gun, S., Manickam, M., Ramakrishnan, B.: A canonical subspace of modular forms of half-integral weight. Math. Ann. 347(4), 899–916 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Knopp, M.: Some new results on the Eichler cohomology of automorphic forms. Bull. AMS 80(4), 607–632 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  11. Knopp, M., Mawi, H.: Eichler cohomology theorem for automorphic forms of small weights. Proc. AMS 138(2), 395–404 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Lawrence, R., Zagier, D.: Modular forms and quantum invariants of \(3\)-manifolds, Sir Michael Atiyah: a great mathematician of the twentieth century. Asian J. Math. 3(1), 93–107 (1999)

    Article  MathSciNet  Google Scholar 

  13. Miyake, T.: Modular Forms. Springer, Berlin (1989)

    Book  MATH  Google Scholar 

  14. Ogg, A.: Modular Forms and Dirichlet Series. Benjamin, New York (1969)

    MATH  Google Scholar 

  15. Razar, M.: Values of Dirichlet series at integers in the critical strip. In: Serre, J.P., Zagier, D. (eds.) Modular Functions of One Variable VI. Lecture Notes in Mathematics. Springer, Berlin (1977)

    Google Scholar 

  16. Sarigedik, Z., Ikikardes, S., Sahin, R.: Power subgroups of the extended Hecke groups. Miskolc Math. Notes 16(1), 483–490 (2015)

    MathSciNet  MATH  Google Scholar 

  17. Shimura, G.: On modular forms of half-integral weight. Ann. Math. 97, 440–481 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yilmaz, Ö., Cangül, N.: On the groups structure and parabolic points of the Hecke group \(H(\lambda )\). Proc. Estonian Acad. Sci. Phys. Math. 55(1), 35–46 (2002)

    MathSciNet  MATH  Google Scholar 

Download references

Author's contributions

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Author information

Authors and Affiliations

  1. Mathematisches Institut, INF 205, Universität Heidelberg, 69120, Heidelberg, Germany

    Winfried Kohnen

  2. Department of Mathematics, 317 A Bliss Hall, American University of Beirut, Beirut, Lebanon

    Wissam Raji

Authors
  1. Winfried Kohnen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wissam Raji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wissam Raji.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kohnen, W., Raji, W. Special values of Hecke L-functions of modular forms of half-integral weight and cohomology. Res Math Sci 5, 22 (2018). https://doi.org/10.1007/s40687-018-0143-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40687-018-0143-3

Search

Navigation