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On the integrality of the Taylor coefficients of mirror maps
, 2007
"... Abstract. We show that the Taylor coefficients of the series q(z) = z exp(G(z)/F(z)) are integers, where F(z) and G(z) + log(z)F(z) are specific solutions of certain hypergeometric differential equations with maximal unipotent monodromy at z = 0. We also address the question of finding the largest ..."
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Cited by 20 (5 self)
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Abstract. We show that the Taylor coefficients of the series q(z) = z exp(G(z)/F(z)) are integers, where F(z) and G(z) + log(z)F(z) are specific solutions of certain hypergeometric differential equations with maximal unipotent monodromy at z = 0. We also address the question of finding the largest
ON POSITIVITY OF TAYLOR COEFFICIENTS OF CONFORMAL MAPS
"... Abstract. We provide an approach to the proof of positivity of the Taylor coecients for a given conformal map of the unit disk onto a plane domain. This short note is a summary of the joint work [2] with Stanis lawa Kanas. 1. ..."
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Abstract. We provide an approach to the proof of positivity of the Taylor coecients for a given conformal map of the unit disk onto a plane domain. This short note is a summary of the joint work [2] with Stanis lawa Kanas. 1.
On the asymptotics of Taylor coefficients of generating functions
, 1998
"... this paper always the main branches of logarithms are taken. It is easy seen that the exponential generating function f(x) = ..."
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this paper always the main branches of logarithms are taken. It is easy seen that the exponential generating function f(x) =
On The Taylor Coefficients Of The Composition Of Two Analytic Functions
, 1996
"... . We give an asymptotic formula for the Taylor coefficients f n of f(z) = l(h(z)) where l(z) is analytic in the unit disc whose Taylor coefficients l n vary `smoothly' and h(z) is analytic in a larger disc. We show that under mild conditions on h(z) , f n ¸ oel [oen] as n ! 1 where oe = 1=h ..."
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Cited by 1 (1 self)
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. We give an asymptotic formula for the Taylor coefficients f n of f(z) = l(h(z)) where l(z) is analytic in the unit disc whose Taylor coefficients l n vary `smoothly' and h(z) is analytic in a larger disc. We show that under mild conditions on h(z) , f n ¸ oel [oen] as n ! 1 where oe = 1=h
ON THE INTEGRALITY OF TAYLOR COEFFICIENTS OF MIRROR MAPS IN SEVERAL VARIABLES
, 2008
"... Abstract. With z = (z1,z2,...,zd), we show that the Taylor coefficients of the multivariable series q(z) = zi exp(G(z)/F(z)) are integers, where F(z) and G(z) + log(zi)F(z), i = 1,2,...,d, are specific solutions of certain systems of Fuchsian differential equations with maximal unipotent monodromy ..."
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Cited by 3 (1 self)
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Abstract. With z = (z1,z2,...,zd), we show that the Taylor coefficients of the multivariable series q(z) = zi exp(G(z)/F(z)) are integers, where F(z) and G(z) + log(zi)F(z), i = 1,2,...,d, are specific solutions of certain systems of Fuchsian differential equations with maximal unipotent monodromy
ON THE INTEGRALITY OF THE TAYLOR COEFFICIENTS OF MIRROR MAPS, II
, 907
"... Abstract. We continue our study begun in “On the integrality of the Taylor coefficients of mirror maps ” (preprint 2007) of the fine integrality properties of the Taylor coefficients of the series q(z) = z exp(G(z)/F(z)), where F(z) and G(z) + log(z)F(z) are specific solutions of certain hypergeome ..."
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Abstract. We continue our study begun in “On the integrality of the Taylor coefficients of mirror maps ” (preprint 2007) of the fine integrality properties of the Taylor coefficients of the series q(z) = z exp(G(z)/F(z)), where F(z) and G(z) + log(z)F(z) are specific solutions of certain
On the Taylor coefficients for powers of the derivative of univalent functions
"... . Let f be a normalized univalent function in the unit disk. We give a necessary condition such that the Koebe function z=(1+z) 2 is an extremal function for the problem of maximizing the modulus of the nth Taylor coefficient of the functions (f 0 ) p , p 2 R. The proof uses an elementary ve ..."
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. Let f be a normalized univalent function in the unit disk. We give a necessary condition such that the Koebe function z=(1+z) 2 is an extremal function for the problem of maximizing the modulus of the nth Taylor coefficient of the functions (f 0 ) p , p 2 R. The proof uses an elementary
New representations of Taylor coefficients of the Weierstrass σfunction
, 909
"... We provide two kinds of representations for the Taylor coefficients of the Weierstrass σfunction σ(·; Γ), where Γ is an arbitrary lattice in C. The first one in terms of HermiteGauss series over Γ and the second one in terms of HermiteGauss integrals over C. As applications, we derive identities ..."
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We provide two kinds of representations for the Taylor coefficients of the Weierstrass σfunction σ(·; Γ), where Γ is an arbitrary lattice in C. The first one in terms of HermiteGauss series over Γ and the second one in terms of HermiteGauss integrals over C. As applications, we derive identities
GROWTH OF TAYLOR COEFFICIENTS OVER COMPLEX HOMOGENEOUS SPACES
"... Abstract. A Hermitian form q on the dual space, g ∗ , of the Lie algebra, g, of a simply connected complex Lie group, G, determines a decreasing family of seminormed spaces J 0 t, t> 0, in the dual of the universal enveloping algebra of g. When q satisfies Hörmander’s condition for the hypoellipt ..."
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for the hypoellipticity of the associated subLaplacian ∆ on G, each J 0 t is a Hilbert space that can be identified as the space of Taylor coefficients of the space of holomorphic functions, f, on G for which (et∆/4f  2)(e) < ∞. The present paper is concerned with the behavior of the Hilbert spaces J 0 t under
Multivariate padic formal congruences and integrality of Taylor coefficients of mirror maps
, 2010
"... We generalise Dwork’s theory of padic formal congruences from the univariate to a multivariate setting. We apply our results to prove integrality assertions on the Taylor coefficients of (multivariable) mirror maps. More precisely, with z = (z1, z2,..., zd), we show that the Taylor coefficients ..."
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Cited by 9 (2 self)
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We generalise Dwork’s theory of padic formal congruences from the univariate to a multivariate setting. We apply our results to prove integrality assertions on the Taylor coefficients of (multivariable) mirror maps. More precisely, with z = (z1, z2,..., zd), we show that the Taylor
Results 1  10
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228,022