Related papers: Note on the Theory of Correlation Functions

We give a completely elementary study for averages of short correlations of so-called sieve functions (a pretty general class of arithmetic functions).

A famous conjecture of Chowla states that the Liouville function $\lambda(n)$ has negligible correlations with its shifts. Recently, the authors established a weak form of the logarithmically averaged Elliott conjecture on correlations of…

We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that above functions are not correlated with finite degree polynomial nilsequences. Besides, we give two…

Hecke operators relate characters of rational conformal field theories (RCFTs) with different central charges, and extend the previously studied Galois symmetry of modular representations and fusion algebras. We show that the conductor $N$…

We prove that arbitrary correlation functions of the H(3)+ model on a sphere have a simple expression in terms of Liouville theory correlation functions. This is based on the correspondence between the KZ and BPZ equations, and on relations…

Kannan Soundararajan recently obtained a new estimate, conditional to the Riemann hypothesis, for the summatory function of the Mobius function. In this expository article we describe his method, with detailed computations.

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

We present an approach that gives rigorous construction of a class of crossing invariant functions in $c=1$ CFTs from the weakly invariant distributions on the moduli space $\mathcal M_{0,4}^{SL(2,\mathbb{C})}$ of $SL(2,\mathbb{C})$ flat…

We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.

The purpose of this note is to report on recent joint work with J. Funke, P. Jenkins, and K. Ono on the traces of CM values of modular functions and some applications.

We present improved Coulomb correction formulae for Bose-Einstein correlations including also exchange term and use them to calculate appropriate correction factors for several source functions. It is found that Coulomb correction to the…

The object of this paper is to study relationship between successive coefficients of some subclasses of the class of univalent functions in the unit disk. the result obtained is sharp, and is used to provide a new, short proof of the…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

We calculate correlation functions in matrix models modified by trace-squared terms. First we study scaling operators in modified one-matrix models and find that their correlation functions satisfy modified Virasoro constraints. Then we…

In this paper we study linear correlations of the divisor function tau(n) = sum_{d|n} 1 using methods developed by Green and Tao. For example, we obtain an asymptotic for sum_{n,d} tau(n) tau(n+d) ... tau(n+ (k-1)d).

In this paper, a new notion, named Riemann-Liouville fractional cosine function is presented. It is proved that a Riemann-Liouville $\alpha$-order fractional cosine function is equivalent to Riemann-Liouville $\alpha$-order fractional…

This note proposes an improved estimate of the coefficient t(n) of the discriminant modular form using elementary method. It improves a well known estimate of the tau function t(n) by Deligne.

In this short note we present a set of interesting and useful properties of a one-parameter family of sequences including factorial and subfactorial, and their relations to the Gamma function and the incomplete Gamma function.

In this paper, usual Sturm-Liouville problems are extended for symmetric functions so that the corresponding solutions preserve the orthogonality property. Two basic examples, which are special cases of a generalized Sturm-Liouville…

I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one point functions of conserved quantities. I…