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NOTES ON THE ARITHMETIC OF HILBERT MODULAR FORMS
"... Shimura proved the following fundamental result (see [37, Theorem 4.3]) on the critical values of the standard Lfunction attached to a holomorphic Hilbert modular form. Theorem 1.1 (Shimura). Let f be a primitive holomorphic Hilbert modular cusp form of type (k, ψ) over a totally real number field ..."
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Shimura proved the following fundamental result (see [37, Theorem 4.3]) on the critical values of the standard Lfunction attached to a holomorphic Hilbert modular form. Theorem 1.1 (Shimura). Let f be a primitive holomorphic Hilbert modular cusp form of type (k, ψ) over a totally real number field
PETERSSON’S TRACE FORMULA AND THE HECKE EIGENVALUES OF HILBERT MODULAR FORMS
"... Abstract. Using an explicit relative trace formula, we obtain a Petersson trace formula for holomorphic Hilbert modular forms. Our main result expresses a sum (over a Hecke eigenbasis) of products of Fourier coefficients and Hecke eigenvalues in terms of generalized Kloosterman sums and Bessel func ..."
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Abstract. Using an explicit relative trace formula, we obtain a Petersson trace formula for holomorphic Hilbert modular forms. Our main result expresses a sum (over a Hecke eigenbasis) of products of Fourier coefficients and Hecke eigenvalues in terms of generalized Kloosterman sums and Bessel
Level optimization in the totally real case
, 2006
"... In this paper, congruences between holomorphic Hilbert modular forms are studied. We show the best possible level optimization result outside ℓ for ℓ≥3 by solving the remaining case of Mazur principle when the degree of the totally real field is even. ..."
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In this paper, congruences between holomorphic Hilbert modular forms are studied. We show the best possible level optimization result outside ℓ for ℓ≥3 by solving the remaining case of Mazur principle when the degree of the totally real field is even.
Quantum unique ergodicity for Eisenstein series on the Hilbert modular group over a totally real field
, 2008
"... W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2,Z)\H. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on PSL(2, O)\H n, where O is the ring ..."
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of integers in a totally real field of degree n over Q with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on nonholomorphic Hilbert modular forms.
Hilbert modular forms and the Ramanujan conjecture
 IN “NONCOMMUTATIVE GEOMETRY AND NUMBER THEORY” ASPECTS OF MATHEMATICS E37, 35–56
, 2003
"... Let F be a totally real field. In this paper we study the Ramanujan Conjecture for Hilbert modular forms and the WeightMonodromy Conjecture for the Shimura varieties attached to quaternion algebras over F. As a consequence, we deduce, at all finite places of the field of definition, the full automo ..."
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Let F be a totally real field. In this paper we study the Ramanujan Conjecture for Hilbert modular forms and the WeightMonodromy Conjecture for the Shimura varieties attached to quaternion algebras over F. As a consequence, we deduce, at all finite places of the field of definition, the full
GALOIS REPRESENTATIONS FOR HOLOMORPHIC SIEGEL MODULAR FORMS
"... Abstract. We prove local global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic HilbertSiegel modular forms in many cases (induced from Borel or Klingen parabolic). For Siegel modular forms, when the local representation is an irreducible principal series ..."
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Abstract. We prove local global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic HilbertSiegel modular forms in many cases (induced from Borel or Klingen parabolic). For Siegel modular forms, when the local representation is an irreducible principal
Nonholomorphic Modular Forms and
 SL(2,R)/U(1) Superconformal Field Theory,” JHEP 1103 (2011) 107 [arXiv:1012.5721 [hepth
"... ar ..."
Overconvergent Hilbert modular forms
 AMER. J. MATH
, 2005
"... We generalize the construction of the eigencurve by ColemanMazur to the setting of totally real fields, and show that a finite slope Hilbert modular eigenform can be deformed into a one parameter family of finite slope eigenforms. The key point is to show the overconvergence of the canonical subgr ..."
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We generalize the construction of the eigencurve by ColemanMazur to the setting of totally real fields, and show that a finite slope Hilbert modular eigenform can be deformed into a one parameter family of finite slope eigenforms. The key point is to show the overconvergence of the canonical
HOLOMORPHIC ALMOST MODULAR FORMS
, 2003
"... Abstract. Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in SL(2, Z). It is proved that such functions have a rotationinvariant limit ..."
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Abstract. Holomorphic almost modular forms are holomorphic functions of the complex upper half plane which can be approximated arbitrarily well (in a suitable sense) by modular forms of congruence subgroups of large index in SL(2, Z). It is proved that such functions have a rotationinvariant limit
TWISTS OF HILBERT MODULAR FORMS
"... Abstract. The theory of newforms for Hilbert modular forms is summarized including a statement of a strong multiplicityone theorem and a characterization of newforms as eigenfunctions for a certain involution whose Dirichlet series has a prescribed Euler product. The general question of twisting ..."
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Abstract. The theory of newforms for Hilbert modular forms is summarized including a statement of a strong multiplicityone theorem and a characterization of newforms as eigenfunctions for a certain involution whose Dirichlet series has a prescribed Euler product. The general question of twisting
Results 1  10
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