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Irregular Primes and Cyclotomic Invariants to 12 Million
TLDR
Computations of irregular primes and associated cyclotomic invariants were extended to all primes up to 12 million using multisectioning/convolution methods and a novel approach which originated in the study of Stickelberger (1996). Expand
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Generalized irregular primes
A prime p > 2 is called irregular , if it divides the numerator of at least one of the Bernoulli numbers B2 , B 4 , …, B p – 3 (in the even suffix notation). The study of irregular primes has itsExpand
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Cyclotomic invariants and $E$-irregular primes
We prove some general results about the Iwasawa invariants X and ,u of the 4pth cyclotomic fileld (p an odd prime), and determine the values of these invariants for p < 104. The properties of X andExpand
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Irregular primes and cyclotomic invariants to four million
Recent computations of irregular primes, and associated cyclotomic invariants, were extended to all primes below four million using an enhanced multisectioning/convolution method. Fermat's "LastExpand
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Computation of the zeros of p -adic L -functions. II
The authors have carried out a computational study of the zeros of Kubota-Leopoldt p-adic L-functions. Results of this study have appeared recently in a previous article. The present paper is aExpand
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A method for computing the Iwasawa -invariant
We present a method for computing the minus-part of the Iwasawa A-invariant of an Abelian field K. Applying this method, we have computed Afor several odd primes p when K runs through a large numberExpand
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On the p-divisibility of Fermat quotients
TLDR
The authors carried out a numerical search for Fermat quotients Q a = (a p-1 - 1)/p vanishing mod p, for 1 ≤ a ≤ p - 1, up to p < 10 6 . Expand
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Cyclotomic invariants for primes to one million
Our recent computation of cyclotomic invariants for primes between 125000 and 150000 was extended to one million. No new phenomena appear. This note is a sequel to our recent report [2] on theExpand
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