Relevant bibliographies by topics / Automorphic forms. Hilbert modular surfaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Automorphic forms. Hilbert modular surfaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Automorphic forms. Hilbert modular surfaces"

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Lee, Min Ho. "Mixed Hilbert modular forms and families of abelian varieties." Glasgow Mathematical Journal 39, no. 2 (1997): 131–40. http://dx.doi.org/10.1017/s001708950003202x.

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In [18] Shioda proved that the space of holomorphic 2-forms on a certain type of elliptic surface is canonically isomorphic to the space of modular forms of weight three for the associated Fuchsian group. Later, Hunt and Meyer [6] made an observation that the holomorphic 2-forms on a more general elliptic surface should in fact be identified with mixed automorphic forms associated to an automorphy factor of the formfor z in the Poincaré upper half plane ℋ, g = and χ(g) = , where g is an element of the fundamental group Γ⊂PSL(2, R) of the base space of the elliptic fibration, χ-Γ→SL(2, R) the m
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Pang Mok, Chung, and Fucheng Tan. "Overconvergent Families of Siegel–Hilbert Modular Forms." Canadian Journal of Mathematics 67, no. 4 (2015): 893–922. http://dx.doi.org/10.4153/cjm-2014-017-9.

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AbstractWe construct one-parameter families of overconvergent Siegel-Hilbert modular forms. This result has applications to the construction of Galois representations for automorphic forms of noncohomological weights.
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Bruggeman, R. W., R. J. Miatello, and I. Pacharoni. "Density results for automorphic forms on Hilbert modular groups." Geometric And Functional Analysis 13, no. 4 (2003): 681–719. http://dx.doi.org/10.1007/s00039-003-0427-6.

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Lee, Min Ho. "Mixed Jacobi-like forms of several variables." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–14. http://dx.doi.org/10.1155/ijmms/2006/31542.

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We study mixed Jacobi-like forms of several variables associated to equivariant maps of the Poincaré upper half-plane in connection with usual Jacobi-like forms, Hilbert modular forms, and mixed automorphic forms. We also construct a lifting of a mixed automorphic form to such a mixed Jacobi-like form.
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Bruggeman, Roelof W., and Roberto J. Miatello. "Density results for automorphic forms on Hilbert modular groups II." Transactions of the American Mathematical Society 362, no. 07 (2010): 3841–81. http://dx.doi.org/10.1090/s0002-9947-10-04974-3.

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Tamiozzo, Matteo. "On the Bloch–Kato conjecture for Hilbert modular forms." Mathematische Zeitschrift 299, no. 1-2 (2021): 427–58. http://dx.doi.org/10.1007/s00209-020-02689-0.

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AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.
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MONKS, KEENAN, SARAH PELUSE, and LYNNELLE YE. "CONGRUENCE PROPERTIES OF BORCHERDS PRODUCT EXPONENTS." International Journal of Number Theory 09, no. 06 (2013): 1563–78. http://dx.doi.org/10.1142/s1793042113500437.

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In his striking 1995 paper, Borcherds [Automorphic forms on Os+2,2(ℝ) and infinite products, Invent. Math.120 (1995) 161–213] found an infinite product expansion for certain modular forms with CM divisors. In particular, this applies to the Hilbert class polynomial of discriminant -d evaluated at the modular j-function. Among a number of powerful generalizations of Borcherds' work, Zagier made an analogous statement for twisted versions of this polynomial. He proves that the exponents of these product expansions, A(n,d), are the coefficients of certain special half-integral weight modular form
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Chiriac, Liubomir. "On the equality case of the Ramanujan Conjecture for Hilbert modular forms." International Journal of Number Theory 15, no. 10 (2019): 2107–14. http://dx.doi.org/10.1142/s179304211950115x.

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The generalized Ramanujan Conjecture for cuspidal unitary automorphic representations [Formula: see text] on [Formula: see text] posits that [Formula: see text]. We prove that this inequality is strict if [Formula: see text] is generated by a Hilbert modular form of weight two, with complex multiplication, and [Formula: see text] is a finite place of degree one. Equivalently, the Satake parameters of [Formula: see text] are necessarily distinct. We also give examples where the equality case does occur for places [Formula: see text] of degree two.
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Aryasomayajula, Anilatmaja, and Baskar Balasubramanyam. "Estimates of automorphic cusp forms over quaternion algebras." International Journal of Number Theory 14, no. 04 (2018): 1143–70. http://dx.doi.org/10.1142/s1793042118500719.

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In this paper, using methods from geometric analysis and theory of heat kernels, we derive qualitative estimates of automorphic cusp forms defined over quaternion algebras. Using which, we prove an average version of the holomorphic QUE conjecture. We then derive quantitative estimates of classical Hilbert modular cusp forms. This is a generalization of the results from [A. Aryasomayajula, Heat kernel approach for sup-norm bounds for cusp forms of integral and half-integral weight, Arch. Math. 106(2) (2016) 165–173; J. S. Friedman, J. Jorgenson and J. Kramer, Uniform sup-norm bounds on average
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Dou, Ze-Li. "On adelic automorphic forms with respect to a quadratic extension." Bulletin of the Australian Mathematical Society 62, no. 1 (2000): 29–43. http://dx.doi.org/10.1017/s000497270001844x.

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Let E/F be a totally real quadratic extension of a totally real algebraic number field. The author has in an earlier paper considered automorphic forms defined with respect to a quaternion algebra BE over E and a theta lift from such quaternionic forms to Hilbert modular forms over F. In this paper we construct adelic forms in the same setting, and derive explicit formulas concerning the action of Hecke operators. These formulas give an algebraic foundation for further investigations, in explicit form, of the arithmetic properties of the adelic forms and of the associated zeta and L-functions.
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Dissertations / Theses on the topic "Automorphic forms. Hilbert modular surfaces"

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Heep, Maria. "Periodenrelationen für GL2(F)." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/20437035.html.

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Ren-He, Su. "The Kohnen plus space for Hilbert-Siegel modular forms." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215374.

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De, Maria Mariagiulia. "Hilbert Modular Forms modulo p of partial weight one and unramifiedness of Galois representations." Thesis, Lille 1, 2020. http://www.theses.fr/2020LIL1I037.

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Cette thèse étudie les formes modulaires de Hilbert de poids arbitraire avec coefficients sur un corps fini de caractéristique p. En particulier, on calcule l’action des opérateurs de Hecke, y compris aux places divisant p où ils ont été construit par Emerton, Reduzzi and Xiao, sur les q-développement géométriques attachés à ces formes. Comme application nous montrons que la représentation galoisienne attachée à une forme propre cuspidale de Hilbert mod p, qui a poids parallel 1 en une place P divisant p, est non-ramifiée en P<br>This thesis studies Hilbert modular forms of arbitrary weight wi
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Liu, Sheng-Chi. "Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1242747349.

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Villanueva, Angel Darío. "Distribución de autovalores de Hecke en cuerpos totalmente reales." Doctoral thesis, 2018. http://hdl.handle.net/11086/11755.

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Sea F un cuerpo de números totalmente real de dimensión d sobre los racionales Q, O_F el anillo de enteros y Gamma(I) un subgrupo de congruencia de Hecke de GL_2(R). Para cada ideal primo p en O_F, p no divida a I, p un cuadrado en el grupo de clases estricto sea T_p el operador de Hecke operando en el espacio de formas cuspidales de Maass en Gamma_(I) \ GL_2(R)^d. El objeto de este trabajo es investigar la distribución conjunta de autovalores de T_p y de los operadores de Casimir C_j en cada componente arquimedeana de F.
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Books on the topic "Automorphic forms. Hilbert modular surfaces"

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Freitag, E. Hilbert modular forms. Springer-Verlag, 1990.

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Holomorphic Hilbert modular forms. Wadsworth & Brooks/Cole Advanced Books & Software, 1990.

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Hilbert modular forms and Iwasawa theory. Clarendon, 2006.

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The 1-2-3 of modular forms: Lectures at a summer school in Nordfjordeid, Norway. Springer, 2008.

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1950-, Goresky Mark, ed. Hilbert modular forms with coefficients in intersection homology and quadratic base change. Birkhäuser, 2012.

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CRM Workshop (1988 Montréal, Québec). The zeta functions of Picard modular surfaces: Based on lectures delivered at a CRM Workshop in the spring of 1988. Les Publications CRM, 1992.

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Freitag, Eberhard. Hilbert Modular Forms. Springer, 1990.

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Freitag, Eberhard. Hilbert Modular Forms. Springer, 2010.

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Darmon, Henri. Elliptic Curves, Hilbert Modular Forms and Galois Deformations. Birkhäuser, 2013.

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10

Hida, Haruzo. Hilbert Modular Forms and Iwasawa Theory (Oxford Mathematical Monographs). Oxford University Press, USA, 2006.

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Book chapters on the topic "Automorphic forms. Hilbert modular surfaces"

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Oda, Takayuki. "The Riemann-Hodge period relation for Hilbert modular forms of weight 2." In Cohomology of Arithmetic Groups and Automorphic Forms. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0085733.

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Harris, Michael. "Period invariants of Hilbert modular forms, I: Trilinear differential operators and L-functions." In Cohomology of Arithmetic Groups and Automorphic Forms. Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0085729.

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Getz, Jayce, and Mark Goresky. "Automorphic Vector Bundles and Local Systems." In Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0351-9_6.

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Getz, Jayce, and Mark Goresky. "The Automorphic Description of Intersection Cohomology." In Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0351-9_7.

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Hirzebruch, F., and D. Zagier. "Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus." In Gesammelte Abhandlungen/Collected Papers. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-61711-9_23.

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Shimura, Goro. "On certain zeta functions attached to two Hilbert modular forms: II. The case of automorphic forms on a quaternion algebra." In Collected Papers. Springer New York, 2003. http://dx.doi.org/10.1007/978-1-4612-2060-2_9.

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Hida, Haruzo. "AUTOMORPHIC FORMS ON INNER FORMS OF GL(2)." In Hilbert Modular Forms and Iwasawa Theory. Oxford University Press, 2006. http://dx.doi.org/10.1093/acprof:oso/9780198571025.003.0002.

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Sczech, Robert. "Cusps on Hilbert Modular Varieties and Values of L-Functions." In Automorphic Forms and Geometry of Arithmetic Varieties. Elsevier, 1989. http://dx.doi.org/10.1016/b978-0-12-330580-0.50009-4.

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Tsuyumine, Shigeaki. "Multi-Tensors of Differential Forms on the Hilbert Modular Variety and on Its Subvarieties, II." In Automorphic Forms and Geometry of Arithmetic Varieties. Elsevier, 1989. http://dx.doi.org/10.1016/b978-0-12-330580-0.50025-2.

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