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Twisted Triple Product $p$-adic $L$-function for Finite Slope Families of Hilbert Modular Forms
Published 24 Jan 2024 in math.NT and math.AG | (2401.13230v2)
Abstract: Let $L$ be a totally real field, and $p$ be a rational prime that is unramified in $L$. We construct overconvergent families of classes of relative de Rham cohomology of the universal abelian scheme over Hilbert modular varieties associated to $L$. We show that these classes come equipped with Gauss-Manin connection. We prove convergence for $p$-adic iteration of this connection, improving upon a technique due to Andreatta-Iovita. We use this to construct a $p$-adic twisted triple product $L$-function associated to finite slope families of Hilbert modular forms, extending work of Blanco-Chacon-Fornea for Hida families.
- Fabrizio Andreatta and Eyal Z. Goren “Hilbert modular forms: mod p𝑝pitalic_p and p𝑝pitalic_p-adic aspects” In Mem. Amer. Math. Soc. 173.819, 2005, pp. vi+100 DOI: 10.1090/memo/0819
- “Katz type p-adic L-functions for primes p non-split in the CM field” arXiv, 2019 DOI: 10.48550/ARXIV.1905.00792
- “Triple product p𝑝pitalic_p-adic L𝐿Litalic_L-functions associated to finite slope p𝑝pitalic_p-adic families of modular forms” In Duke Math. J. 170.9, 2021, pp. 1989–2083 DOI: 10.1215/00127094-2020-0076
- Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni “p𝑝pitalic_p-adic families of Siegel modular cuspforms” In Ann. of Math. (2) 181.2, 2015, pp. 623–697 DOI: 10.4007/annals.2015.181.2.5
- Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni “On overconvergent Hilbert modular cusp forms” In Astérisque, 2016, pp. 163–193
- Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni “The adic, cuspidal, Hilbert eigenvarieties” In Res. Math. Sci. 3, 2016, pp. Article No. 34 DOI: 10.1186/s40687-016-0076-7
- Fabrizio Andreatta, Adrian Iovita and Vincent Pilloni “Le halo spectral” In Ann. Sci. Éc. Norm. Supér. (4) 51.3, 2018, pp. 603–655 DOI: 10.24033/asens.2362
- Fabrizio Andreatta, Adrian Iovita and Glenn Stevens “Overconvergent modular sheaves and modular forms for 𝐆𝐋2/Fsubscript𝐆𝐋2𝐹{\bf GL}_{2/F}bold_GL start_POSTSUBSCRIPT 2 / italic_F end_POSTSUBSCRIPT” In Israel J. Math. 201.1, 2014, pp. 299–359 DOI: 10.1007/s11856-014-1045-8
- Jon Aycock “Families of Differential Operators for Overconvergent Hilbert Modular Forms” arXiv, 2020 DOI: 10.48550/ARXIV.2006.02543
- Massimo Bertolini, Henri Darmon and Kartik Prasanna “Generalized Heegner cycles and p𝑝pitalic_p-adic Rankin L𝐿Litalic_L-series” With an appendix by Brian Conrad In Duke Math. J. 162.6, 2013, pp. 1033–1148 DOI: 10.1215/00127094-2142056
- “Twisted triple product p𝑝pitalic_p-adic L𝐿Litalic_L-functions and Hirzebruch-Zagier cycles” In J. Inst. Math. Jussieu 19.6, 2020, pp. 1947–1992 DOI: 10.1017/s1474748019000021
- “Notes on Crystalline Cohomology. (MN-21)” Princeton University Press, 2015 DOI: doi:10.1515/9781400867318
- Robert F. Coleman “Classical and overconvergent modular forms” In Invent. Math. 124.1-3, 1996, pp. 215–241 DOI: 10.1007/s002220050051
- Robert F. Coleman “p𝑝pitalic_p-adic Banach spaces and families of modular forms” In Invent. Math. 127.3, 1997, pp. 417–479 DOI: 10.1007/s002220050127
- “Singularités des espaces de modules de Hilbert, en les caractéristiques divisant le discriminant” In Compositio Math. 90.1, 1994, pp. 59–79 URL: http://www.numdam.org.pros2.lib.unimi.it/item?id=CM_1994__90_1_59_0
- “Diagonal cycles and Euler systems I: A p𝑝pitalic_p-adic Gross-Zagier formula” In Ann. Sci. Éc. Norm. Supér. (4) 47.4, 2014, pp. 779–832 DOI: 10.24033/asens.2227
- Eyal Z. Goren “Hasse invariants for Hilbert modular varieties” In Israel J. Math. 122, 2001, pp. 157–174 DOI: 10.1007/BF02809897
- Andrew Graham, Vincent Pilloni and Joaquín Rodrigues Jacinto “p-adic interpolation of Gauss–Manin connections on nearly overconvergent modular forms and p-adic L-functions”, 2023 arXiv:2311.14438 [math.NT]
- Giacomo Graziani “Modular sheaves of de Rham classes on Hilbert formal modular schemes for unramified primes” arXiv, 2020 DOI: 10.48550/ARXIV.2007.15997
- Haruzo Hida “p𝑝pitalic_p-adic automorphic forms on Shimura varieties”, Springer Monographs in Mathematics Springer-Verlag, New York, 2004, pp. xii+390 DOI: 10.1007/978-1-4684-9390-0
- Haruzo Hida “On p𝑝pitalic_p-adic L𝐿Litalic_L-functions of GL(2)×GL(2)GL2GL2{\rm GL}(2)\times{\rm GL}(2)roman_GL ( 2 ) × roman_GL ( 2 ) over totally real fields” In Ann. Inst. Fourier (Grenoble) 41.2, 1991, pp. 311–391 URL: http://www.numdam.org.pros2.lib.unimi.it/item?id=AIF_1991__41_2_311_0
- Michael Harris and Stephen S. Kudla “The central critical value of a triple product L𝐿Litalic_L-function” In Ann. of Math. (2) 133.3, 1991, pp. 605–672 DOI: 10.2307/2944321
- “Gauss-Manin connections for p𝑝pitalic_p-adic families of nearly overconvergent modular forms” In Ann. Inst. Fourier (Grenoble) 64.6, 2014, pp. 2449–2464 DOI: 10.5802/aif.2916
- Atsushi Ichino “Trilinear forms and the central values of triple product L𝐿Litalic_L-functions” In Duke Math. J. 145.2, 2008, pp. 281–307 DOI: 10.1215/00127094-2008-052
- Nicholas M. Katz “p𝑝pitalic_p-adic interpolation of real analytic Eisenstein series” In Ann. of Math. (2) 104.3, 1976, pp. 459–571 DOI: 10.2307/1970966
- Nicholas M. Katz “p𝑝pitalic_p-adic L𝐿Litalic_L-functions for CM fields” In Invent. Math. 49.3, 1978, pp. 199–297 DOI: 10.1007/BF01390187
- Zheng Liu “Nearly overconvergent Siegel modular forms” In Ann. Inst. Fourier (Grenoble) 69.6, 2019, pp. 2439–2506 URL: http://aif.cedram.org/item?id=AIF_2019__69_6_2439_0
- Toshitsune Miyake “On automorphic forms on GL2subscriptGL2{\rm GL}_{2}roman_GL start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT and Hecke operators” In Ann. of Math. (2) 94, 1971, pp. 174–189 DOI: 10.2307/1970741
- Santiago Molina “Finite slope triple product p𝑝pitalic_p-adic L𝐿Litalic_L-functions over totally real number fields” In J. Number Theory 223, 2021, pp. 267–306 DOI: 10.1016/j.jnt.2020.11.013
- M. Rapoport “Compactifications de l’espace de modules de Hilbert-Blumenthal” In Compositio Math. 36.3, 1978, pp. 255–335 URL: http://www.numdam.org.pros2.lib.unimi.it/item?id=CM_1978__36_3_255_0
- Goro Shimura “The special values of the zeta functions associated with Hilbert modular forms” In Duke Math. J. 45.3, 1978, pp. 637–679 URL: http://projecteuclid.org.pros2.lib.unimi.it/euclid.dmj/1077312955
- “p𝑝pitalic_p-adic cohomology and classicality of overconvergent Hilbert modular forms” In Astérisque, 2016, pp. 73–162
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