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- Joe Buhler, Richard E. Crandall, Reijo Ernvall, Tauno Metsänkylä, Amin Shokrollahi
- J. Symb. Comput.
- 2001

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)

- Reijo Ernvall, Tauno Metsänkylä
- Math. Comput.
- 1997

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.

- TAUNO METSÄNKYLÄ
- 2003

Catalan’s Conjecture predicts that 8 and 9 are the only consecutive perfect powers among positive integers. The conjecture, which dates back to 1844, was recently proven by the Swiss mathematician Preda Mihăilescu. A deep theorem about cyclotomic fields plays a crucial role in his proof. Like Fermat’s problem, this problem has a rich history with some… (More)

- Tauno Metsänkylä
- 2010

The values of the first factor Hx(m) of the class number of the with cyclotomic field are tabulated for 120 composite rre's larger than 100. A conjecture concerning a divisibility property of Hx{m) is stated.

- R. ERNVALL, T. METSÄNKYLÄ
- 2010

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 a sequel to that article, dealing with the computation of the zeros under certain conditions that complicate the original situation.

- By R. Ernvall, T. Metsänkylä
- 2010

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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