Related papers: On the representation of number-theoretic function…
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when $f = \Lambda$ and $f = \tau$,…
One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler…
We investigate the possibilities to calculate vector partition functions by means of iterated partial fraction decomposition, as suggested by Beck (2004). Particularly, for an important type of families of rational functions, we describe an…
The Dirichlet forms methods, in order to represent errors and their propagation, are particularly powerful in infinite dimensional problems such as models involving stochastic analysis encountered in finance or physics, cf. [5]. Now, coming…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
This paper introduces a symbolic calculus-based approach for deriving closed-form expressions for the sums of arithmetic sequences. The method extends beyond constant-difference sequences to those with polynomially increasing steps,…
Our results concern analytic functions on the open unit $p$-adic poly-disc in $\mathbb{C}^n_p$ centered at the multiplicative unit and we prove that such functions only vanish at finitely many $n$-tuples of roots of unity…
Different questions lead to the same class of functions from natural integers to integers: those which have integral difference ratios, i.e. verifying $f(a)-f(b)\equiv0 \pmod {(a-b)}$ for all $a>b$. We characterize this class of functions…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer…
In this paper, we evaluate the following families of definite integrals in closed form and we show that they are expressible only in terms of the dilogarithm function and the inverse tangent integral, and elementary functions.…
We compute the critical $L$-values of some weight 3, 4, or 5 modular forms, by transforming them into integrals of the complete elliptic integral $K$. In doing so, we prove closed form formulas for some moments of $K'^3$. Many of our…
By simple elementary method,we obtain with ease,a highly simple expression for the remainder term of the divisor problem and use it to obtain an Euler-Maclaurin analogue of summation involving divisor function.We also obtain a relation…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
We study several variants of Euler sums by using the methods of contour integration and residue theorem. These variants exhibit nice properties such as closed forms, reduction, etc., like classical Euler sums. In addition, we also define a…
We study the distributions of values of the logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main object is determining and investigating the density functions of such value-distributions for any…
Let $k$ be a fixed finite geometric extension of the rational function field $\mathbb{F}_q(t)$. Let $F/k$ be a finite abelian extension such that there is an $\Fq$-rational place $\infty$ in $k$ which splits in $F/k$ and let $\mathcal{O}_F$…
In this paper, by using the method of Contour Integral Representations and the Theorem of Residues and integral representations of series, we discuss the analytic representa- tions of parametric Euler sums that involve harmonic numbers…