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Hecke Operators and Derivatives of L-Functions

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Compositio Mathematica

Abstract

In this paper, we introduce a new way of studying derivatives of L-functions of cusp forms by associating to them cocycles analogous, in function, to the period polynomial. The main result gives a description of the effect of Hecke operators on these cocycles.

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References

  • [A] Antoniadis, J. A.: Modulformen auf Γ00N) mit rationalen Perioden, Manuscripta. Math. 74 (1992), 359-384.

    Google Scholar 

  • [CZ] Choie, Yj. and Zagier, D.: Rational period functions for PSL(2, Z), Contemp. Math. 143 (1993), 89–108.

    Google Scholar 

  • [D] Diamantis, N.: Special values of higher derivatives of L-functions, Forum Math. 11 (1999), 229–252.

  • [G] Goldfeld, D.: Special values of derivatives of L-functions, In: CMS Conf. Proc. 15 Amer. Math. Soc., Providence, 1995, pp. 245–282.

  • [H] Haberland, K.: Perioden von Modulformen einer Variabler and Gruppencohomologie. I, Math. Nachr. 112 (1983), 159–173.

    Google Scholar 

  • [K] Knopp, M.: Rational period functions of the modular group, Duke Math. J. 45 (1978), 47–62.

    Google Scholar 

  • [M] Manin, Y. T.: Periods of parabolic points and p-adic Hecke series, Math. Sb. (1973), 371–393.

  • [S] Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions, Princeton University Press, 1971.

  • [Sk] Skoruppa, N. P.: Binary quadratic forms and the Fourier coef¢cients of elliptic and Jacobi modular forms, J. Reine angew. Math. 411 (1990), 66–95.

    Google Scholar 

  • [Z] Zagier, D.: Hecke operators and periods of modular forms, In: Israel Math. Conf. Proc. 3, Bar-Ilan Univ., Ramat gan, 1990, pp. 321–336.

    Google Scholar 

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Diamantis, N. Hecke Operators and Derivatives of L-Functions. Compositio Mathematica 125, 39–54 (2001). https://doi.org/10.1023/A:1002648306247

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  • DOI: https://doi.org/10.1023/A:1002648306247

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