Related papers: Note on on Dedekind type DC sums
Within the realm of QCD sum rules, one of the most important areas of application of this nonperturbative approach is the prediction of the decay constants of heavy mesons. However, in spite of the fact that, indisputably, the adopted…
In this paper we have discussed convergence of power series both in p-adic norm as well as real norm. We have investigated rational summability of power series with respect to both p-adic norm and real norm under certain conditions. Then we…
New cases of the multiplicity conjecture are considered.
We obtain closed form of some infinite series involving derivatives of an analogue of the Riemann xi function for Dedekind zeta function and nontrivial zeros of Dedekind zeta function assuming the Extended Riemann Hypothesis. Conversely, we…
We obtain new bounds, pointwisely and on average, for Dedekind sums $\mathsf{s}(\lambda,p)$ modulo a prime $p$ with $\lambda$ of small multiplicative order $d$ modulo $p$. Assuming the infinitude of Mersenne primes, the range of our results…
In a recent note W. Kohnen asks whether the values of Dedekind sums are dense in the field of $p$-adic numbers. The present paper answers this question. Dedekind sums do not approximate units of $\mathbb Z_2$ or $\mathbb Z_3$, so they are…
We summarize some recent work on large-Nc sum rules.
A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this volume of Modern Physics Letters A. Collectively, these papers constitute the proceedings…
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
Wolstenholme's type summations involve certain powers of all residues $k$ modulo some prime number $p$. We first consider the sums of double or triple products of certain powers of all residues, e.g., the sums of the terms $(a+k)^m(b+k)^n$…
This note presents selected values of definite integrals whose integrand contains a power of the Dedekind function having imaginary argument.
We obtain some new inequalities of Chebyshev Type.
We use Poisson summation formula to calculate integrals of producs of sinc functions (cf. [4]) and related integrals as in [5] and [3]. We also generalize the one in [5] and introduce other remarkable integrals. Finally we give a sum…
In this paper we introduce the notion of the $P$-sequences and apply their properties in studying representability of real numbers. Another application of $P$-sequences we find in generating the Prouhet-Tarry-Escott pairs.
It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of…
In this article we present certain formulas involving arithmetical functions. In the first part we study properties of sums and product formulas for general type of arithmetic functions. In the second part we apply these formulas to the…
We prove that the greedy sum of a direct product of two numeric arrays of complex numbers is equal to the product of the greedy sums of the factors provided that all the mentioned sums exist.
We study some basic properties of sofic-Dyck shifts and finite-type-Dyck shifts. We prove that the class of sofic-Dyck shifts is stable under proper conjugacies. We prove a Decomposition Theorem of a proper conjugacy between edge-Dyck…
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
In this paper, we consider infinite sums derived from the reciprocals of the generalized Fibonacci numbers. We obtain some new and interesting identities for the generalized Fibonacci numbers.