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The space of toroidal automorphic forms was introduced by Zagier in 1979. Let F be a global field. An automorphic form on GL(2) is toroidal if it has vanishing constant Fourier coefficients along all ...
Renormdynamics, multiparticle production, negative binomial distribution and Riemann zeta function
Renormdynamics multiparticle production negative binomial distribution Riemann zeta function
2011/3/1
Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.
Schur function expansions of KP tau functions associated to algebraic curves
Schur function expansions of KP tau functions algebraic curves
2011/2/21
The Schur function expansion of Sato-Segal-Wilson KP τ -functions is reviewed. The case of
τ -functions related to algebraic curves of arbitrary genus is studied in detail.
We show that for a transcendental entire function the set of points whose orbit under iteration is bounded can have arbitrarily small positive Hausdorff dimension.
Behavior of the singular solutions of the problem governed by the adjunct of the Laplace operator affected by a weight function near the tops of plane polygon
Singularity Polygon function
2010/9/21
In this work, we study the behavior of the singular solutions of the problem governed by the adjunct of the laplacian operator affected by a weight function in a polygon. First, the study will be done...
On an elliptic boundary problem governed by a Laplacian operator perturbed by a spectral parameter and affected by a weight function in a plane polygon
Spectral prameter Polygon
2010/9/21
In this work, we study the problem governed by the laplacian operator perturbed by a spectral parameter and affected by a weight function in a polygon. First, the study will be done in a plane sector....
A family of fractional integrals pertaining to multivariable I-function
Fractional integral Eulerian integral
2010/9/25
The object of this paper is to derive an Eulerian integral and a main theorem based upon the fractional operator associated with ¯H -function [3] and multivariable I-function [4] which provide un...
A generalization of the implicit function theorem
Implicit Function Theorem convex subsets Banach spaces
2010/9/25
In this work, we generalize the classical theorem of the implicit function, for functions whose domains are open subset of Banach spaces in to a Banach space, to the case of functions whose domains ar...
We have dramatically extended the zero eld susceptibility series at both high and low temperature of the Ising model on the square, triangular and honeycomb lattices, and used these data to calculate...
Unitary representations of a loop ax+b group, Wiener measure and Gamma-function
Unitary representations loop ax+b group Wiener measure Gamma-function
2011/2/24
We construct a family of irreducible unitary representations of the loop affine group of a line (ax+b group) with central extension on the Hilbert space of square integrable functions with respect to ...
Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure
Igusa's p-adic local zeta function associated polynomial mapping polynomial integration measure
2011/2/25
For p prime, we give an explicit formula for Igusa’s local zeta function associated to a polynomial mapping f = (f1, . . . , ft) : Qn p ! Qt p,with f1, . . . , ft 2 Zp[x1, . . . , xn], and an integrat...
The twisting representation of the $L$-function of a curve
twisting representation $L$-function of a curve
2011/2/21
Let C be a smooth projective curve defined over a number field k and let C′ be a twist of C. For every isomorphism : C′! C defined over a finite Galois extension L/k, we introduce a rational Artin re...
L^3 estimates for an algebraic variable coefficient Wolff circular maximal function
L^3 estimates algebraic variable coefficient Wolff circular maximal function
2011/1/17
In 1997, Thomas Wol proved sharp L3 bounds for his circular maximal function, and in 1999, Kolasa and Wol proved certain non-sharp Lp inequalities for a broader class of maximal functions arising fr...
The Hirota τ-function and well-posedness of the KdV equation with an arbitrary step like initial profile decaying on the right half line
Korteweg-de Vries equation inverse scattering transform Schr ¨odinger operator
2011/3/1
We are concerned with the Cauchy problem for the KdV equation on the whole line with an initial profile V0 which is decaying sufficiently fast at +¥ and arbitrarily enough (i.e., no decay or patte...
Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
suprema of Gaussian processes omega results random multiplicative function
2011/1/17
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic,but supply strong information when one is only ...