AbstractWe consider some implications of the generalized Riemann hypothesis using Ihara's zeta function on infinite unramified Galois extensions of number fields. Our main result is, assuming the generalized Riemann hypothesis, that there is a positive constant c such that for any prime number p ≫ 0 there is a prime q < c(log p)2 such that qp − 1≢ 1 (mod p2)
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
AbstractLet p be an odd prime and suppose that for some a, b, c ϵ Z\pZ we have that ap + bp + cp = 0...
AbstractWe show how to compute the values of h1(p), the first factor of the class number of the cycl...
AbstractEmploying a technique introduced by Gallagher, a simple derivation is given of Montgomery's ...
AbstractLetkbe a real abelian number field with Galois groupΔandpan odd prime number. Denote byk∞the...
AbstractWe show that the abc-conjecture of Masser and Oesterlé implies that there are infinitely man...
AbstractWe prove more special cases of the Fontaine–Mazur conjecture regardingp-adic Galois represen...
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(...
Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of an algebraic number field $k$. We denot...
AbstractLet k=Q(−2379) and knr,2 be the maximal unramified 2-extension of k. To show that knr,2/k is...
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(...
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(...
Let $k$ be a number field, $p$ a prime, and $k^{nr,p}$ the maximal unramified $p$-extension of $k$. ...
AbstractThe Fontaine–Mazur Conjecture for number fields predicts that infinite ℓ-adic analytic group...
AbstractBoston [2] asked a question concerning the existence of unramifiedp-extensions, which is clo...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
AbstractLet p be an odd prime and suppose that for some a, b, c ϵ Z\pZ we have that ap + bp + cp = 0...
AbstractWe show how to compute the values of h1(p), the first factor of the class number of the cycl...
AbstractEmploying a technique introduced by Gallagher, a simple derivation is given of Montgomery's ...
AbstractLetkbe a real abelian number field with Galois groupΔandpan odd prime number. Denote byk∞the...
AbstractWe show that the abc-conjecture of Masser and Oesterlé implies that there are infinitely man...
AbstractWe prove more special cases of the Fontaine–Mazur conjecture regardingp-adic Galois represen...
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(...
Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of an algebraic number field $k$. We denot...
AbstractLet k=Q(−2379) and knr,2 be the maximal unramified 2-extension of k. To show that knr,2/k is...
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(...
For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q)≅G and disc(...
Let $k$ be a number field, $p$ a prime, and $k^{nr,p}$ the maximal unramified $p$-extension of $k$. ...
AbstractThe Fontaine–Mazur Conjecture for number fields predicts that infinite ℓ-adic analytic group...
AbstractBoston [2] asked a question concerning the existence of unramifiedp-extensions, which is clo...
integer a # * 1, or a perfect square, there exist infinitely many primes p for which a is a primiti...
AbstractLet p be an odd prime and suppose that for some a, b, c ϵ Z\pZ we have that ap + bp + cp = 0...
AbstractWe show how to compute the values of h1(p), the first factor of the class number of the cycl...
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