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THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET $L$ -FUNCTIONS OVER RATIONAL FUNCTION FIELDS

  • GORAN DJANKOVIĆ (a1)

Abstract

We prove the reciprocity law for the twisted second moments of Dirichlet $L$ -functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet $L$ -functions over $\mathbb{Q}$ obtained by Conrey [‘The mean-square of Dirichlet $L$ -functions’, arXiv:0708.2699 [math.NT] (2007)] and Young [‘The reciprocity law for the twisted second moment of Dirichlet $L$ -functions’, Forum Math. 23(6) (2011), 1323–1337].

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This work was partially supported by the Ministry of Education, Science and Technological Development of Republic of Serbia, Project no. 174008.

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[1] Bettin, S., ‘On the reciprocity law for the twisted second moment of Dirichlet L-functions’, Trans. Amer. Math. Soc. 368(10) (2016), 68876914.
[2] Blomer, V. and Khan, R., ‘Twisted moments of $L$ -functions and spectral reciprocity’, arXiv:1706.01245 (2017).
[3] Blomer, V., Li, X. and Miller, S. D., ‘A spectral reciprocity formula and non-vanishing for $L$ -functions on $\text{GL}(4)\times \text{GL}(2)$ ’, arXiv:1705.04344 (2017).
[4] Conrey, J. B., ‘The mean-square of Dirichlet $L$ -functions’, arXiv:0708.2699 [math.NT] (2007).
[5] Rosen, M., Number Theory in Function Fields, Graduate Texts in Mathematics, 210 (Springer, New York, NY, 2000).
[6] Young, M. P., ‘The reciprocity law for the twisted second moment of Dirichlet L-functions’, Forum Math. 23(6) (2011), 13231337.
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THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET $L$ -FUNCTIONS OVER RATIONAL FUNCTION FIELDS

  • GORAN DJANKOVIĆ (a1)

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