## 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

## Abstract:

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

*p*th 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: https://doi.org/10.1090/S0025-5718-1992-1122068-3
- MathSciNet review: 1122068