We give an introduction to zeta functions over nite elds, focusing on moment zeta functions and zeta functions of a ne toric hypersurfaces.

We have recently described molecular changes in T cells from tumor-bearing patients that are associated with depressed immune function. The present work investigates changes in T-cell signal transduction proteins including the T-cell receptor-zeta (TCR-zeta) chain and receptor-associated tyrosine kinases in patients with metastatic malignant melanoma. A marked decrease in the expression of the ...

We present a non-perturbative method for calculating the abundance of primordial black holes given an arbitrary one-point probability distribution function curvature perturbation, $P(\zeta)$. A is essential when considering non-Gaussianities that cannot be treated using conventional perturbative expansion. To determine full statistics density field, we relate $\zeta$ to Gaussian field by equati...

Let F be an algebraic number field. Recently, L. Weng introduced zeta functions of rank n associated to F as a generalization of the Iwasawa-Tate zeta integral from the Arakelov geometric point of view. In the article, we call them the Weng zeta function of rank n. In the case of rank one, the Weng zeta function coincide with the Dedekind zeta function of F . The background and precise definiti...

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.

The Riemann zeta process is a stochastic process {Z(σ), σ > 1} with independent increments and marginal distributions whose characteristic functions are proportional to the Riemann zeta function along vertical lines < s = σ . We establish functional limit theorems for the zeta process and other related processes as arguments σ approach the pole at s = 1 of the zeta function (from above).

High-level ab initio quantum-mechanical methods have been used to study the HFS molecule. The most advanced method involves a triple-zeta plus double polarization plusf functions (TZ2P +f, basis set in conjunction with the singleand double-excitation coupled-cluster method perturbatively including connected triple excitations, i.e., CCSD (T) . Two of the three fundamental vibrational frequencie...

The multiplicative anomaly, recently introduced in QFT, plays a fundamental role in solving some mathematical inconsistencies of the widely used zeta-function regularization method. Its physical relevance is still an open question and is here analyzed in the light of a non-perturbative method. Even in this approach the “different physics” seems to hold and not to be easily removable by renormal...

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two P(φ)2 systems with polynomial self-interactions.