1,570 research outputs found
Orthogonal Ramanujan Sums, its properties and Applications in Multiresolution Analysis
Signal processing community has recently shown interest in Ramanujan sums
which was defined by S.Ramanujan in 1918. In this paper we have proposed
Orthog- onal Ramanujan Sums (ORS) based on Ramanujan sums. In this paper we
present two novel application of ORS. Firstly a new representation of a finite
length signal is given using ORS which is defined as Orthogonal Ramanujan
Periodic Transform.Secondly ORS has been applied to multiresolution analysis
and it is shown that Haar transform is a spe- cial case
A Burgess-like subconvex bound for twisted L-functions
Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, X a primitive character of conductor q, and s a point on the critical line Rs = 1/2. It is proved that
L(g circle times chi, s) 0
is arbitrary and theta = 7/64 is the current known approximation towards the RamannJan-Petersson conjecture (which would allow theta = 0); moreover, the dependence on s and all the parameters of g is polynomial. This result is an analog of Burgess' classical subconvex bound for Dirichlet L-functions. In Appendix 2 the above result is combined with a theorem of Waldspurger and the adelic calculations of Baruch-Mao to yield an improved uniform upper bound for the Fourier coefficients of holomorphic half-integral weight cusp forms
Multiple Gamma Function and Its Application to Computation of Series
The multiple gamma function , defined by a recurrence-functional
equation as a generalization of the Euler gamma function, was originally
introduced by Kinkelin, Glaisher, and Barnes around 1900. Today, due to the
pioneer work of Conrey, Katz and Sarnak, interest in the multiple gamma
function has been revived. This paper discusses some theoretical aspects of the
function and their applications to summation of series and infinite
products.Comment: 20 pages, Latex, uses kluwer.cls, will appear in The Ramanujan
Journa
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