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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computation of the zeros of $p$-adic $L$-functions
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by R. Ernvall and T. Metsänkylä PDF
Math. Comp. 58 (1992), 815-830 Request permission


The authors have computed the zeros of the Kubota-Leopoldt p-adic L-functions ${L_p}(s,\chi )$ for some small odd primes p and for a number of Dirichlet characters $\chi$. The zeros of the corresponding Iwasawa power series ${f_\theta }(T)$ are also computed. The characters $\chi$ (associated with quadratic extensions of the pth cyclotomic field) are chosen so as to cover as many different splitting types of ${f_\theta }(T)$ as possible. The $\lambda$-invariant of this power series, equal to its number of zeros, assumes values up to 8. The article is a report on these computations and their results, including the required theoretical background. Much effort is devoted to a study of the accuracy of the computed approximations.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 815-830
  • MSC: Primary 11R23; Secondary 11R42, 11Y70
  • DOI:
  • MathSciNet review: 1122068