Related papers: Formule de Trace pour le Anneaux de Witt

We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Salem type and some linear recurrent sequences of Pisot type.…

The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

Periodic orbit expressions for the density of states lead to spurious results when directly used to calculate quantities of thermodynamic interest. This is because the trace formula is usually valid only for large energies while the…

Extending a classical estimate of Mertens for the sum of the reciprocals of the first primes, we provide an explicit remainder formula for products of an arbitrary, but fixed, number of primes.

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…

The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard fundamentals will be given. For some…

We generalize condensed motives, through Witt vectors and the associated moduli stacks of generalized line bundles.

In this paper we discuss a method to express the Prime counting function as a "sum" over Non-trivial zeros of Riemann Zeta function, using techniques from Analytic Number Theory, also we apply our results to the sum over primes of any…

In this note, we present a simple summation formula for $k$-bonacci numbers. The derivation consists in obtaining the generating function of such numbers, and noting that its evaluation at a particular value yields a formula generalizing a…

Explicit descriptions of local integral Galois module generators in certain extensions of $p$-adic fields due to Pickett have recently been used to make progress with open questions on integral Galois module structure in wildly ramified…

Relying on the Hurwitz formula, we find sums of the series over sine and cosine functions through the Hurwitz zeta function. Using another summation formula for these trigonometric series, we find finite sums of some series over the Riemann…

In the first part, we consider generalized quadratic Gauss sums as finite analogues of the Jacobi theta function, and the reciprocity law for Gauss sums as their transformation formula. We attach finite Dirichlet series to Gauss sums using…

In this paper we extend and apply the work of Paul Balmer and others on derived and triangular Witt Groups. We obtain a generalized form of d\'{e}vissage for derived Witt Groups over Cohen-Macaulay rings.

In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…

We derive a closed form for the generalized Bernoulli polynomial of order $n$ in terms of Bell polynomials and Stirling numbers of the second kind using the Fa\`a di Bruno's formula.

In this note we provide a simple formula of general term of recurrent sequence.

Trace formulae for d-regular graphs are derived and used to express the spectral density in terms of the periodic walks on the graphs under consideration. The trace formulae depend on a parameter w which can be tuned continuously to assign…

We give a short proof of the trace formula for Hecke operators on modular forms for the modular group, using the action of Hecke operators on the space of period polynomials.

In this paper we give a factorization theorem for the ring of exponential polynomials in many variables over an algebraically closed field of characteristic 0 with an exponentiation. This is a generalization of the factorization theorem due…

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and then we obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace…