Hybrid subconvexity for class group 𝐿-functions and uniform sup norm bounds of Eisenstein series

References

[1] E. Assing, On sup-norm bounds part II: GL⁢(2) Eisenstein series, Forum Math. 31 (2019), no. 4, 971–1006. 10.1515/forum-2018-0014Search in Google Scholar

[2] V. Blomer, Non-vanishing of class group L-functions at the central point, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 4, 831–847. 10.5802/aif.2035Search in Google Scholar

[3] V. Blomer, Epstein zeta-functions, subconvexity, and the purity conjecture, J. Inst. Math. Jussieu 19 (2020), no. 2, 581–596. 10.1017/S1474748018000142Search in Google Scholar

[4] V. Blomer, G. Harcos and P. Michel, Bounds for modular L-functions in the level aspect, Ann. Sci. Éc. Norm. Supér. (4) 40 (2007), no. 5, 697–740. 10.1016/j.ansens.2007.05.003Search in Google Scholar

[5] S. Dittmer, M. Proulx and S. Seybert, Some arithmetic problems related to class group L-functions, Ramanujan J. 37 (2015), no. 2, 257–268. 10.1007/s11139-014-9562-ySearch in Google Scholar

[6] W. Duke, J. Friedlander and H. Iwaniec, Class group L-functions, Duke Math. J. 79 (1995), no. 1, 1–56. 10.1215/S0012-7094-95-07901-0Search in Google Scholar

[7] W. Duke, J. B. Friedlander and H. Iwaniec, The subconvexity problem for Artin L-functions, Invent. Math. 149 (2002), no. 3, 489–577. 10.1007/s002220200223Search in Google Scholar

[8] W. Duke, O. Imamoḡlu and A. Tóth, Cycle integrals of the j-function and mock modular forms, Ann. of Math. (2) 173 (2011), no. 2, 947–981. 10.4007/annals.2011.173.2.8Search in Google Scholar

[9] W. Duke, O. Imamoḡlu and A. Tóth, Geometric invariants for real quadratic fields, Ann. of Math. (2) 184 (2016), no. 3, 949–990. 10.4007/annals.2016.184.3.8Search in Google Scholar

[10] Y. Hu and A. Saha, Sup-norms of eigenfunctions in the level aspect for compact arithmetic surfaces, preprint (2019), https://arxiv.org/abs/1905.06295. Search in Google Scholar

[11] B. Huang and Z. Xu, Sup-norm bounds for Eisenstein series, Forum Math. 29 (2017), no. 6, 1355–1369. 10.1515/forum-2015-0195Search in Google Scholar

[12] H. Iwaniec, Spectral Methods of Automorphic Forms, 2nd ed., Grad. Stud. Math. 53, American Mathematical Society, Providence, 2002. 10.1090/gsm/053Search in Google Scholar

[13] H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ. 53, American Mathematical Society, Providence, 2004. 10.1090/coll/053Search in Google Scholar

[14] H. Iwaniec and P. Sarnak, L∞ norms of eigenfunctions of arithmetic surfaces, Ann. of Math. (2) 141 (1995), no. 2, 301–320. 10.2307/2118522Search in Google Scholar

[15] P. Michel and A. Venkatesh, Heegner points and non-vanishing of Rankin/Selberg L-functions, Analytic Number Theory, Clay Math. Proc. 7, American Mathematical Society, Providence (2007), 169–183. Search in Google Scholar

[16] P. Michel and A. Venkatesh, The subconvexity problem for GL2, Publ. Math. Inst. Hautes Études Sci. (2010), no. 111, 171–271. 10.1007/s10240-010-0025-8Search in Google Scholar

[17] P. Sarnak, Arithmetic quantum chaos, The Schur Lectures (1992), Israel Math. Conf. Proc. 8, Bar-Ilan University, Ramat Gan (1995), 183–236. Search in Google Scholar

[18] P. C. Sarnak, Class numbers of indefinite binary quadratic forms. II, J. Number Theory 21 (1985), no. 3, 333–346. 10.1016/0022-314X(85)90060-5Search in Google Scholar

[19] P. Söhne, An upper bound for Hecke zeta-functions with Groessencharacters, J. Number Theory 66 (1997), no. 2, 225–250. 10.1006/jnth.1997.2167Search in Google Scholar

[20] N. Templier, Heegner points and Eisenstein series, Forum Math. 23 (2011), no. 6, 1135–1158. 10.1515/form.2011.041Search in Google Scholar

[21] E. C. Titchmarsh, On Epstein’s Zeta-Function, Proc. London Math. Soc. (2) 36 (1934), 485–500. 10.1112/plms/s2-36.1.485Search in Google Scholar

[22] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, 2nd ed., Oxford University, New York, 1986. Search in Google Scholar

[23] H. Wu, Burgess-like subconvexity for GL1, Compos. Math. 155 (2019), no. 8, 1457–1499. 10.1112/S0010437X19007309Search in Google Scholar

[24] H. Wu and N. Andersen, Explicit subconvexity for GL2 and some applications, preprint (2018), https://arxiv.org/abs/1812.04391. Search in Google Scholar

[25] M. P. Young, Weyl-type hybrid subconvexity bounds for twisted L-functions and Heegner points on shrinking sets, J. Eur. Math. Soc. (JEMS) 19 (2017), no. 5, 1545–1576. 10.4171/JEMS/699Search in Google Scholar

[26] M. P. Young, A note on the sup norm of Eisenstein series, Q. J. Math. 69 (2018), no. 4, 1151–1161. 10.1093/qmath/hay019Search in Google Scholar

[27] S.-W. Zhang, Gross–Zagier formula for GL2, Asian J. Math. 5 (2001), no. 2, 183–290. 10.4310/AJM.2001.v5.n2.a1Search in Google Scholar

[28] S.-W. Zhang, Gross-Zagier formula for GL⁢(2). II, Heegner Points and Rankin L-Series, Math. Sci. Res. Inst. Publ. 49, Cambridge University, Cambridge (2004), 191–214. 10.1017/CBO9780511756375.008Search in Google Scholar