DOI QR코드

DOI QR Code

ON SOME EXACT RECIPROCITY FORMULAS FOR TWISTED SECOND MOMENTS OF DIRICHLET L-FUNCTIONS

  • Received : 2011.05.30
  • Published : 2012.09.30

Abstract

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

Acknowledgement

Supported by : Ministry of Science

References

  1. L. Carlitz, Some theorems on generalized Dedekind sums, Pacic J. Math. 3 (1953), 513-522. https://doi.org/10.2140/pjm.1953.3.513
  2. J. B. Conrey, The mean-square of Dirichlet L-functions, arXiv:0708.2699v1.
  3. R. R. Hall, J. Wilson, and D. Zagier, Reciprocity formulae for general Dedekind- Rademacher sums, Acta Arith. 73 (1995), no. 4, 389-396. https://doi.org/10.4064/aa-73-4-389-396
  4. S. Kanemitsu, J. Ma, and W. Zhang, On the discrete mean value of the product of two Dirichlet L-functions, Abh. Math. Semin. Univ. Hambg. 79 (2009), no. 2, 149-164. https://doi.org/10.1007/s12188-009-0016-1
  5. M. Young, The reciprocity law for the twisted second moment of Dirichlet L-functions, Forum Mathematicum, to appear, DOI: 10.1515/FORM.2011.053.