共查询到20条相似文献,搜索用时 15 毫秒
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Andrei Jorza 《Mathematische Annalen》2013,355(1):381-400
We prove local–global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert–Siegel modular forms in many cases (induced from Borel or Klingen parabolic), and as a corollary we obtain a conjecture of Skinner and Urban. For Siegel modular forms, when the local representation is an irreducible principal series we get local–global compatibility without a twist. We achieve this by proving a version of rigidity (strong multiplicity one) for GSp(4) using, on the one hand the doubling method to compute the standard L-function, and on the other hand the explicit classification of the irreducible local representations of GSp(4) over p-adic fields; then we use the existence of a globally generic Hilbert–Siegel modular form weakly equivalent to the original and we refer to Sorensen (Mathematica 15:623–670, 2010) for local–global compatibility in that case. 相似文献
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Publications mathématiques de l'IHÉS - We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation... 相似文献
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Recent works have used the theory of modular forms to establishlinear congruences for the partition function and for tracesof singular moduli. We show that this type of phenomenon iscompletely general, by finding similar congruences for the coefficientsof any weakly holomorphic modular form on any congruence subgroup 相似文献
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The Ramanujan Journal - We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level p with $$11 \le p \le 37$$ with... 相似文献
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P. Guerzhoy 《Proceedings of the American Mathematical Society》2008,136(9):3051-3059
We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.
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In this article, we study the nature of zeros of weakly holomorphic modular forms. In particular, we prove results about transcendental zeros of modular forms of higher levels and for certain Fricke groups which extend a work of Kohnen (Comment Math Univ St Pauli 52:55–57, 2003). Furthermore, we investigate the algebraic independence of values of weakly holomorphic modular forms. 相似文献
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G. V. Voskresenskaya 《Mathematical Notes》2000,67(2):129-137
In the paper we find the metacyclic groups of the form 〈a, b:a
m=e, b
s=e, b
−1
ab=a
r〉, wherem=3, 4, 5, 7, 11, 23, such that the modular forms associated with all elements of these groups by some faithful representation
are multiplicative η-products.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 163–173, February, 2000. 相似文献
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Shunsuke Yamana 《Mathematische Annalen》2009,344(4):853-862
We prove that Siegel modular forms of degree greater than one, integral weight and level N, with respect to a Dirichlet character of conductor are uniquely determined by their Fourier coefficients indexed by matrices whose contents run over all divisors of . The cases of other major types of holomorphic modular forms are included.
The author is supported by the Grant-in-Aid for JSPS fellows. 相似文献
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Duke and Jenkins (Pure Appl Math Q 4(4):1327–1340, 2008) constructed a canonical basis for the space of weakly holomorphic modular forms for \({{\rm SL}_2(\mathbb{Z})}\) and investigated the zeros of the basis elements. In this paper we give an analogy in the Drinfeld setting of the result given by Duke and Jenkins (Pure Appl Math Q 4(4):1327–1340, 2008). 相似文献
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We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan τ-function, and use this to prove that these Fourier coefficients are often highly divisible by 2. 相似文献
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For holomorphic modular forms on tube domains, there are two types of known Fourier expansions, i.e. the classical Fourier
expansion and the Fourier-Jacobi expansion. Either of them is along a maximal parabolic subgroup. In this paper, we discuss
Fourier expansion of holomorphic modular forms on tube domains of classical type along the minimal parabolic subgroup. We
also relate our Fourier expansion to the two known ones in terms of Fourier coefficients and theta series appearing in these
expansions. 相似文献
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