The triple reciprocity law for the twisted second moments of Dirichlet 𝐿-functions over function fields

Djanković, Goran; Đokić, Dragan; Lelas, Nikola

doi:10.1090/proc/15507

The triple reciprocity law for the twisted second moments of Dirichlet $L$-functions over function fields
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by Goran Djanković, Dragan Đokić and Nikola Lelas

Proc. Amer. Math. Soc. 149 (2021), 2851-2860

DOI: https://doi.org/10.1090/proc/15507

Published electronically: April 29, 2021

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Abstract:

We obtain the reciprocity formula for twisted second moments of Dirichlet $L$-functions over rational function fields involving three different irreducible moduli. This is a function field analogue of the formula discovered by Bettin over $\mathbb {Q}$.

References

Nickolas Andersen and Eren Mehmet Kıral, Level reciprocity in the twisted second moment of Rankin-Selberg $L$-functions, Mathematika 64 (2018), no. 3, 770–784. MR 3826486, DOI 10.1112/s0025579318000256
Sandro Bettin, On the reciprocity law for the twisted second moment of Dirichlet $L$-functions, Trans. Amer. Math. Soc. 368 (2016), no. 10, 6887–6914. MR 3471080, DOI 10.1090/tran/6771
Valentin Blomer and Rizwanur Khan, Twisted moments of $L$-functions and spectral reciprocity, Duke Math. J. 168 (2019), no. 6, 1109–1177. MR 3934595, DOI 10.1215/00127094-2018-0060
Valentin Blomer and Rizwanur Khan, Uniform subconvexity and symmetry breaking reciprocity, J. Funct. Anal. 276 (2019), no. 7, 2315–2358. MR 3912807, DOI 10.1016/j.jfa.2018.11.009
Valentin Blomer, Xiaoqing Li, and Stephen D. Miller, A spectral reciprocity formula and non-vanishing for $L$-functions on $\textrm {GL}(4)\times \textrm {GL}(2)$, J. Number Theory 205 (2019), 1–43. MR 3996341, DOI 10.1016/j.jnt.2019.05.011
J. B. Conrey, The mean-square of Dirichlet $L$-functions, preprint, 2007, arXiv:0708.2699.
Goran Djanković, The reciprocity law for the twisted second moment of Dirichlet $L$-functions over rational function fields, Bull. Aust. Math. Soc. 98 (2018), no. 3, 383–388. MR 3877269, DOI 10.1017/S0004972718000874
Goran Djanković, Dragan Đokić, Nikola Lelas, and Ilija Vrećica, The integrated fourth moment of Dirichlet $L$-functions over rational function fields, J. Number Theory 218 (2021), 334–369. MR 4157703, DOI 10.1016/j.jnt.2020.07.001
Jonathan P. Keating and Zeév Rudnick, The variance of the number of prime polynomials in short intervals and in residue classes, Int. Math. Res. Not. IMRN 1 (2014), 259–288. MR 3158533, DOI 10.1093/imrn/rns220
Michael Rosen, Number theory in function fields, Graduate Texts in Mathematics, vol. 210, Springer-Verlag, New York, 2002. MR 1876657, DOI 10.1007/978-1-4757-6046-0
Atle Selberg, Contributions to the theory of Dirichlet’s $L$-functions, Skr. Norske Vid.-Akad. Oslo I 1946 (1946), no. 3, 62. MR 22872
Matthew P. Young, The reciprocity law for the twisted second moment of Dirichlet $L$-functions, Forum Math. 23 (2011), no. 6, 1323–1337. MR 2855052, DOI 10.1515/FORM.2011.053
Raphaël Zacharias, Periods and reciprocity I, Int. Math. Res. Not. IMRN 3 (2021), 2191–2209. MR 4206609, DOI 10.1093/imrn/rnz100