A New approach to q-zeta function

By Taekyun Kim. 2005

48 citations recorded by the source corpus.

We construct the new q-extension of Bernoulli numbers and polynomials in this paper. Finally we consider the q-zeta functions which interpolate the new q-extension of Bernoulli numbers and polynomials.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/124fc2314072b5ce7d6714c026ebb960eb36ed5c

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In Algebra and Number Theory

1. Yilmaz Simsek
2. Taekyun Kim
3. Veli Kurt
4. Daeyeoul Kim
5. I. N. Cangul
6. Hacer Ozden
7. Mümün Can
8. Mehmet Cenkci

In Applied Mathematics

1. Yilmaz Simsek
2. Veli Kurt
3. Daeyeoul Kim
4. I. N. Cangul
5. Hacer Ozden
6. Taekyun Kim
7. Hari M. Srivastava

Citations in the corpus

• New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials (2007, methodology): “([14]) For h ∈ Z, q ∈ Cp with | 1 − q |p< p − 1 p−1 , we have ∫”
• Twisted Dedekind Type Sums Associated with Barnes' Type Multiple Frobenius-Euler l-Functions (2007, background): “If ζ → 1, B (h) j,ζ (q)→ B (h) j (q), which are the numbers defined by Kim [27].”
• A note on p-adic q-Euler measure (2007, background): “We say that f is a uniformly differentiable function at a point a ∈ Zp, and write f ∈ UD(Zp), if the difference quotient Ff (x, y) = f(x)− f(y) x− y has a limit f́(a) as (x, y) → (a, a).”
• Complete sum of products of (h, q)-extension of Euler polynomials and numbers (2010, methodology): “Bernoulli and Euler numbers and polynomials were studied by many authors (see for detail [18], [19], [ 9 ], [7], [10], [11], [12], [13], [16], [8], [20], [21], [22], [24], [14]) . We introduce some of them here.”
• Multiple p-adic L-function (2005, unknown): “These p-adic L-functions interpolate the values Lp(1− n, χ) = − 1 n (1− χn(p)p )Bn,χn , for n ∈ N = {1, 2, · · · , } , where Bn,χ denote the nth generalized Bernoulli numbers associated with the primitive Dirichlet character χ, and χn = χw , with w the Teichmüller character, cf.[1-24].”
• Twisted (h,q)-Bernoulli numbers and polynomials related to twisted (h,q)-zeta function and L-function☆ (2006, methodology): “If w → 1, then B n,w(z, q) → B n (z, q) and F (h) w,q(t, z) → F (h) q (t, z) = F (h) q (t)e [14].”