Polynomial characteristic functions for $GF(p)$ and irregular primes
نویسندگان
چکیده
منابع مشابه
Irregular primes to 163 million
We compute all irregular primes less than 163 577 856. For all of these primes we verify that the Kummer–Vandiver conjecture holds and that the λ-invariant is equal to the index of irregularity.
متن کاملRelationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...
متن کاملSIGNED GENERALIZED PETERSEN GRAPH AND ITS CHARACTERISTIC POLYNOMIAL
Let G^s be a signed graph, where G = (V;E) is the underlying simple graph and s : E(G) to {+, -} is the sign function on E(G). In this paper, we obtain k-th signed spectral moment and k-th signed Laplacian spectral moment of Gs together with coefficients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.
متن کاملCharacteristic Polynomial
A [ An−1 + p1A n−2 + · · ·+ pn−1 In ] = −pn In . Since A is nonsingular, pn = (−1)n det(A) 6= 0; thus the result follows. Newton’s Identity. Let λ1, λ2, . . . , λn be the roots of the polynomial K(λ) = λ + p1λ n−1 + p2λ n−2 + · · · · · ·+ pn−1λ+ pn. If sk = λ k 1 + λ k 2 + · · ·+ λn, then pk = − 1 k (sk + sk−1 p1 + sk−2 p2 + · · ·+ s2 pk−2p1 + s1 pk−1) . Proof. From K(λ) = (λ − λ1)(λ − λ2) . . ...
متن کاملOn the counting function of irregular primes
It is well-known that there are infinitely many irregular primes. We prove a quantitative version of this statement, namely the number of such primes p ≤ x is at least (1 + o(1)) log log x/ log log log x as x → ∞. We show that the same conclusion holds for the irregular primes corresponding to the Euler numbers. Under some conditional results from diophantine approximation, the above lower boun...
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: Rocky Mountain Journal of Mathematics
سال: 1978
ISSN: 0035-7596
DOI: 10.1216/rmj-1978-8-4-583