Related papers: Modular Inverse and Reciprocity Formula

The Fourier transform is naturally defined for integrable functrions. Otherwise, it should be stipulated in which sense the Fourier transform is understood. We consider some class of radial and, generally saying, nonintegrable functions.…

The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by $z^{s-1}$, along geodesics connecting two cusps. This setting generalizes simultaneously the…

We derive product and series representations of the gamma function using Newton interpolation series. Using these identities, a new formula for the coefficients in the Taylor series of the reciprocal gamma function is found. We also find…

In this paper, a classification of modules of the intermediate series over the twisted N=2 superconformal algebra is obtained.

The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase…

An identity is proved connecting two finite sums of inverse tangents. This identity is discretized version of Jacobi's imaginary transformation for the modular angle from the theory of elliptic functions. Some other related identities are…

We derive a formula for the the modular class of a Lie algebroid with a regular twisted Poisson structure in terms of a canonical Lie algebroid representation of the image of the Poisson map. We use this formula to compute the modular…

In this paper will be considered standard forms of generalized inverses for matrices in the shape of block representations {1, 2, 3, 4, 5, 5^k}-inverse. Especially will be considered Moore-Penrose inverse and the group inverse. Results from…

We prove a formula for special L-values of Anderson's modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of L-series.

We obtain an equivariant class formula for z-deformation of t-modules. Under mild conditions, it allows us to get an equivariant class formula for t-modules.

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.

This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…

We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.

In the recent article by Feng et al. [Science 333, 729-733 (2011)] a system is proposed with a periodic spatial modulation of refractive index and absorption. It is claimed that this system is nonreciprocal and can be used as an optical…

In this paper, we introduce the notion of weak core and central weak core inverse in a {\it proper $*$-ring}. We further elaborate on these two classes by producing a few representations and characterizations of the weak core and central…

This paper provides some statistics for the coefficients of Russell- Type modular equations for the modular function, {\lambda}({\tau}). The results hold uniformly for all odd primes. They do not rely on any numerical evaluations of…

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

The problem of applying Nash-Moser Newton methods to obtain periodic solutions of the compressible Euler equations has led authors to identify the main obstacle, namely, how to invert operators which impose periodicity when they are based…

We prove recursive formulas involving sums of divisors and sums of triangular numbers and give a variety of identities relating arithmetic functions to divisor functions providing inductive identities for such arithmetic functions.

We give explicit structure of the graded ring of modular forms with respect to Gamma(N) (N=1,2,3,4,5,6,7,8,9,10,12,16,18) and for some other congruence groups. We also study the modular forms of half-integer weight for certain groups.