Harmonic analysis of the functions $\tildeΔ(x)$ and $N(T)$
In this paper, under the Riemann hypothesis, we study the Fourier analysis about the functions $\tildeΔ(x)$ and $N(T)$ .
math.NT↗
arXiv subjects
Jining Gao
Publications and source records attributed to Jining Gao.
On the representations of $N(T)$ via prime numbers
In this paper, under the RH, we give a new representation of $N(T)$ in term of sum of the logarithms of the powers of prime numbers and compute the difference between the new representation and Guinand representation.
math.GM↗
Acid zeta function and ajoint acid zeta function
In this paper we set up the theory of acid zeta function and ajoint acid zeta function, based on the theory, we point out a reason to doubt the truth of the Riemann hypothesis and also as a consequence, we give out some new RH equivalences.
math.GM↗
Some sufficient conditions of a given series with rational terms converging to an irrational number or a transcdental number
In this paper, we propose various sufficient conditions to determine if a given real number is an irrational number or a transcendental number and also apply these conditions to some interesting examples, particularly,one of them comes from complex analytic dynamics
math.NT↗
On the tensor structure of BRST differential and it's application
In this paper,we compute tensor structure of BRST differential and use this tensor representation we give out $CL_{\infty}$ algebra differential and $GA_{\infty}$ differential which are generalization of Chevalley-Eilenberg differential and Hochchild differential respectively.
math.QA↗
$L_{\infty}$ algebra structures of Lie algebra deformations
In this paper,we will show how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into Strong homotopy Lie algebra or $L_{\infty}$ algebra. All such obstructions have been transfered to the revelvant $L_{\infty}$ algebras which contain only three terms
math.QA↗
The Maurer-Cartan structure of BRST differential
In this paper, we construct a new sequence of generators of the BRST complex and reformulate the BRST differential so that it acts on elements of the complex much like the Maurer-Cartan differential acts on left-invariant forms. Thus our BRST differential is formally analogous to the differential defined on the BRST formulation of the Chevalley-Eilenberg cochain complex of a Lie algebra. Moreover, for an important class of physical theories, we show that in fact the differential is a Chevalley-Eilenberg differential. As one of the applications of our formalism, we show that the BRST differential provides a mechanism which permits us to extend a nonintegrable system of vector fields on a manifold to an integrable system on an extended manifold.
math-ph↗
Chain extensions of D-algebras and their applications
In order to unify the methods which have been applied to various topics such as BRST theory of constraints, Poisson brackets of local functionals, and certain developments in deformation theory, we formulate a new concept which we call the {\it chain extension} of a $D$-algebra. We develop those aspects of this new idea which are central to applications to algebra and physics. Chain extensions may be regarded as generalizations of ordinary algebraic extensions of Lie algebras. Applications of our theory provide a new constructive approach to BRST theories which only contains three terms; in particular, this provides a new point of view concerning consistent deformations. Finally, we show how Lie algebra deformations are encoded into the structure maps of an sh-Lie algebra with three terms.
math.QA↗