Volume 103, Issue 1
April 1993, pages 1-103
pp 1- April 1993
pp 1-25 April 1993
Transformation formula for exponential sums involving fourier coefficients of modular forms
In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular groupSL(2, ℤ). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups ofSL(2, ℤ) and prove similar estimates for the corresponding Dirichlet series.
pp 27-39 April 1993
DirichletL-function and power series for Hurwitz zeta function
For 0 < α < 1, letζ(s, α) be the Hurwitz zeta function and let ζ_{1} (s, α) = ζ(s, α) -α− s. For a fixeds, we developζ_{1}(s,α) as a power series in α in the complex circle ¦α¦ < 1. If$$\sum\limits_{\chi \left( {\bmod q} \right)} {L\left( {s,\chi } \right)L\left( {s',\bar \chi } \right)} = \frac{{\phi \left( q \right)}}{{q^{s + s'} }}\sum\limits_{k/q} \mu \left( {\frac{q}{k}} \right)\left( {\sum\limits_{a = 1}^k {\left( {\frac{k}{a}} \right)^{\operatorname{Re} s + \operatorname{Re} s'} + Q\left( {s,s',k} \right)} } \right)$$, we obtain an asymptotic expansion for Q(k) =Q(s,s′,k) using the power series forζ_{1}(s,α)
pp 41-71 April 1993
Determinants of parabolic bundles on Riemann surfaces
LetX be a compact Riemann surface andM_{s}^{p}(X) the moduli space of stable parabolic vector bundles with fixed rank, degree, rational weights and multiplicities. There is a natural Kähler metric onM_{s}^{p}(X). We obtain a natural metrized holomorphic line bundle onM_{s}^{p}(X) whose Chern form equalsmr times the Kähler form, wherem is the common denominator of the weights andr the rank.
pp 73-89 April 1993
Convolution properties of some classes of meromorphic univalent functions
Convolution technique and subordination theorem are used to study certain class of meromorphic univalent functions in the punctured unit disc.
pp 91-96 April 1993
New operational relations between the original and the image for two-dimensional Laplace transforms involving a general class of polynomials, Fox’sH-function and the multivariableH-function are obtained. The result provides a unification of the bivariate Laplace transforms for theH-functions given by Chaurasia [2, 3].
pp 97-102 April 1993
Some applications of Briot—Bouquet differential subordination
Subhas S Bhoosnurmath S R Swamy
Some applications of Briot—Bouquet differential subordination are obtained which improve or extend a number of classical results in the univalent function theory.
pp 103-103 April 1993
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