Related papers: Multiple q-zeta values and traces

In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…

We study graded traces of vectors in free bosonic vertex operator algebras and lattice vertex operator algebras. We show in particular that trace functions in these two theories always have the shape f(q)/\eta(q)^d where f(q) is…

We consider a particular one-parameter family of q-analogues of multiple zeta values. The intrinsic q-regularisation permits an extension of these q-multiple zeta values to negative integers. Renormalised multiple zeta values satisfying the…

Multiple zeta values (MZVs) are generalizations of Riemann zeta values at positive integers to multiple variable setting. These values can be further generalized to level $N$ multiple polylog values by evaluating multiple polylogs at $N$-th…

In this paper, we introduce the symmetric multiple Eisenstein series, a variant of the multiple Eisenstein series. As a fundamental result, we show that they satisfy the linear shuffle relation. As a case study, we investigate the vector…

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such…

Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two…

The MZV algebra is the graded algebra over ${\bold Q}$ generated by all multiple zeta values. The stable derivation algebra is a graded Lie algebra version of the Grothendieck-Teichm\"{u}ller group. We shall show that there is a canonical…

For each prime $\ell$, let $|\cdot|_\ell$ be an extension to $\bar \Q$ of the usual $\ell$-adic absolute value on $\Q$. Suppose $g(z) = \sum_{n=0}^\infty c(n)q^n \in M_{k+\half}(N)$ is an eigenform whose Fourier coefficients are algebraic…

Recently, Bruinier and Ono proved that the coefficients of certain weight -1/2 harmonic weak Maa{\ss} forms are given as "traces" of singular moduli for harmonic weak Maa{\ss} forms. Here, we prove that similar results hold for the…

In a recent work, the author has constructed two families of algebraic cycles in Bloch cycle algebra over the prjective line minus 3 points that are expected to correspond to multiple polylogarithms in one variable and have a good…

In this paper we construct a modular form f of weight one attached to an imaginary quadratic field K. This form, which is non-holomorphic and not a cusp form, has several curious properties. Its negative Fourier coefficients are non-zero…

Recently, the present authors jointly with Tauraso found a family of binomial identities for multiple harmonic sums (MHS) on strings $(\{2\}^a,c,\{2\}^b)$ that appeared to be useful for proving new congruences for MHS as well as new…

Motivated by the 1920's seminal work of Major MacMahon, Amdeberhan--Andrews--Tauraso recently introduced an infinite family of $q$-series \[ \mathcal{U}_{t}(a;q):= \sum_{1\le n_1<n_2<\cdots<n_t}…

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.

This survey gives a self-contained introduction to q-analogues of multiple zeta values (qMZVs). For this, we consider most common models of qMZVs in a unified setup going back to Bachmann and K\"uhn, such as a related quasi-shuffle product…

Zagier's well-known work on traces of singular moduli relates the coefficients of certain weakly holomorphic modular forms of weight $1/2$ to traces of values of the modular $j$-function at imaginary quadratic points. A real quadratic…

Answering problems of Manin, we use the critical $L$-values of even weight $k\geq 4$ newforms $f\in S_k(\Gamma_0(N))$ to define zeta-polynomials $Z_f(s)$ which satisfy the functional equation $Z_f(s)=\pm Z_f(1-s)$, and which obey the…

We consider the structure functions S^(q)(T), i.e. the moments of order q of the increments X(t+T)-X(t) of the Foreign Exchange rate X(t) which give clear evidence of scaling (S^(q)(T)~T^z(q)). We demonstrate that the nonlinearity of the…

We compute the Quot and finitized Coh zeta functions of the inert quadratic orders $\mathbb{F}_q[[T]]+T^{m}\mathbb{F}_{q^{2}}[[T]]$ for every $m\geq 1$ in terms of a $2m$-fold multisum, and then show this multisum equals an $m$-fold…