相关论文: On the relevance of the multiplicative anomaly
In a recent work, S. Dowker has shed doubt on a recipe used in computing the partition function for a matrix valued operator. This recipe, advocated by Benson, Bernstein and Dodelson, leads naturally to the so called multiplicative anomaly…
The multiplicative anomaly related to the functional regularized determinants involving products of elliptic operators is introduced and some of its properties discussed. Its relevance concerning the mathematical consistency is stressed.…
When dealing with zeta-function regularized functional determinants of matrix valued differential operators, an additional term, overlooked until now and due to the multiplicative anomaly, may arise. The presence and physical relevance of…
We discuss the role of the multiplicative anomaly for a complex scalar field at finite temperature and density. It is argued that physical considerations must be applied to determine which of the many possible expressions for the effective…
The global multiplicative properties of Laplace type operators acting on irreducible rank one symmetric spaces are considered. The explicit form of the multiplicative anomaly is derived and its corresponding value is calculated exactly, for…
In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to…
In this note we investigate mixed partitions with extra condition on the sizes of the blocks. We give a general formula and the generating function. We consider in more details a special case, determining the generating functions, some…
In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with $k$-regular partitions. Extending the generating function for $k$-regular partitions…
The functional determinant multiplicative anomaly, or defect, is more closely investigated and explicit forms for products of linear operators are produced. I also present formulae for the defect of products of second order operators in…
Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any $n\neq 7$. The basis for this is an inequality for the partition function which…
Matrix multiplication (hereafter we use the acronym MM) is among the most fundamental operations of modern computations. The efficiency of its performance depends on various factors, in particular vectorization, data movement and arithmetic…
We present a natural multiplicative theory of integer partitions (which are usually considered in terms of addition), and find many theorems of classical number theory arise as particular cases of extremely general combinatorial structure…
For the case of a relativistic scalar field at finite temperature with a chemical potential, we calculate an exact expression for the one-loop effective action using the full fourth order determinant and zeta-function regularisation. We…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
In studying the complexity of iterative processes it is usually assumed that the arithmetic operations of addition, multiplication, and division can be performed in certain constant times. This assumption is invalid if the precision…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
Fibonacci numbers can be expressed in terms of multinomial coefficients as sums over integer partitions into odd parts. We use this fact to introduce a family of double inequalities involving the generating function for the number of…
A new recursive procedure for calculation of restricted partition function is suggested. An explicit formula for the restricted partition function is found based on this procedure.
In this paper, we investigate decompositions of the partition function $p(n)$ from the additive theory of partitions considering the famous M\"{o}bius function $\mu(n)$ from multiplicative number theory. Some combinatorial interpretations…
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement…