相关论文: The multiplicative anomaly for determinants revisi…

Lecomte and Ovsienko constructed $SL_{n+1}(R)$-equivariant quantization maps $Q_\lambda$ for symbols of differential operators on $\lambda$-densities on $\RP^n$. We derive some formulas for the associated graded equivariant star products…

In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of…

\begin{abstract} By following the paradigm of the global quantisation, instead of the analysis under changes of coordinates, in this work we establish a global analysis for the explicit computation of the Dixmier trace and the Wodzicki…

We provide symmetrization results in the form of mass concentration comparisons for fractional singular elliptic equations in bounded domains, coupled with homogeneous external Dirichlet conditions. Two types of comparison results are…

We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…

We prove asymptotic formulas for the complex coefficients of $(\zeta q;q)_\infty^{-1}$, where $\zeta$ is a root of unity, and apply our results to determine secondary terms in the asymptotics for $p(a,b,n)$, the number of integer partitions…

In the paper we show that for a normal-crossings degeneration $Z$ over the ring of integers of a local field with $X$ as generic fibre, the local monodromy operator and its powers determine invariant cocycle classes under the decomposition…

In this work we prove the local multiplicity at most one theorem underlying the definition and theory of local $\gamma$-, $\epsilon$- and $L$-factors, defined by virtue of the generalized doubling method, over any local field of…

We study an extension of the Distributive Full Non-associative Lambek Calculus with iterative division operators. The iterative operators can be seen as representing iterative composition of linguistic resources or of actions. A complete…

The aim of this paper is to derive a summation formula for the alternating infinite series and an expression for zeta function by using hyperbolic secant random variables. These identities involve Euler numbers and are obtained by computing…

In this article we consider a class of non-degenerate elliptic operators obtained by superpositioning the Laplacian and a general nonlocal operator. We study the existence-uniqueness results for Dirichlet boundary value problems, maximum…

For every, possibly unbounded, multiplication operator in $L^p$-space, $p\in ]0,\infty[$, on finite separable measure space we show that multicyclicity, multi-*-cyclicity, and multiplicity coincide. This result includes and generalizes…

We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…

If the zeta function regularization is used and a complex mass term considered for fermions, the phase does not appear in the fermion determinant. This is not a drawback of the regularization, which can recognize the phase through source…

In this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when…

We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out that they have a very different combinatorial behavior. We…

The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also…

We introduce a noncommutative analogue of the absolute value of a regular operator acting on a noncommutative $\mathrm{L}^p$-space. We equally prove that two classical operator norms, the regular norm and the decomposable norm are…

Two multiplicative anomalies are evaluated for the determinant of the conformal higher spin propagating operator on spheres given by Tseytlin. One holds for the decomposition of the higher derivative product into its individual second order…

For $n$ a nonnegative integer, we consider the $n$-Laplacian $\Delta_n$ acting on the space of $n$-differentials on a confinite Riemann surface $X$ which has ramification points. The trace formula for the resolvent kernel is developed along…