Binomial polynomials mimicking Riemann's zeta function
نویسندگان
چکیده
منابع مشابه
The Arakawa–kaneko Zeta Function and Poly-bernoulli Polynomials
The purpose of this paper is to introduce a generalization of the Arakawa–Kaneko zeta function and investigate their special values at negative integers. The special values are written as the sums of products of Bernoulli and poly-Bernoulli polynomials. We establish the basic properties for this zeta function and their special values.
متن کاملThe zeta function, L-functions, and irreducible polynomials
= 1 1− q1−s , where we have convergence for all s with <(s) > 1. This automatically gives us analytic continuation of ζ to all of C. We note the following simple observations: 1. The Riemann hypothesis: All zeroes of ζ lie on the line <(s) = 1/2, simply because there are no zeroes! 2. ζ has poles at s = 1 + 2πin log q . 3. Locally around s = 1, ζ has the Laurent series expansion: 1 (s− 1) log q...
متن کاملShifted Jack Polynomials , Binomial Formula , and Applications
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [ x i ( xi ∂ ∂xi + (n− j)θ + u )]
متن کاملThe binomial formula for nonsymmetric Macdonald polynomials
The q-binomial theorem is essentially the expansion of (x − 1)(x − q) · · · (x − q) in terms of the monomials x. In a recent paper [O], A. Okounkov has proved a beautiful multivariate generalization of this in the context of symmetric Macdonald polynomials [M1]. These polynomials have nonsymmetric counterparts [M2] which are of substantial interest, and in this paper we establish nonsymmetric a...
متن کاملA Class of Binomial Permutation Polynomials
For a prime power q, let Fq be the finite field with q elements and F ∗ q denote its multiplicative group. A polynomial f ∈ Fq[x] is called a permutation polynomial (PP) if its associated polynomial mapping f : c 7→ f(c) from Fq to itself is a bijection. A permutation polynomial f(x) is referred to as a complete permutation polynomial (CPP) if f(x)+x is also a permutation over Fq [4]. Permutati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Integral Transforms and Special Functions
سال: 2020
ISSN: 1065-2469,1476-8291
DOI: 10.1080/10652469.2020.1755672