Tauno Metsänkylä

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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 codes (Shokrollahi, 1996). The latter idea reduces the problem to that of finding zeros of a polynomial over Fp of degree < (p− 1)/2(More)
The authors carried out a numerical search for Fermat quotients Qa = (ap−1 − 1)/p vanishing mod p, for 1 ≤ a ≤ p − 1, up to p < 106. This article reports on the results and surveys the associated theoretical properties of Qa. The approach of fixing the prime p rather than the base a leads to some aspects of the theory apparently not published before.
We prove some general results about the Iwasawa invariants \ and u of the 4pth cyclotomic field (p an odd prime), and determine the values of these 4 — — invariants for p < 10 . The properties of A. and u are closely connected with the ¿i-irregularity (i.e. the irregularity with respect to the Euler numbers) of p. 4 A list of all ¿i-irregular primes less(More)
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