Výsledky vyhledávání - "Knospe, Heiko"

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Special values of $p$-adic $L$-functions and Iwasawa $\lambda$-invariants of Dirichlet characters

Autor: Knospe, Heiko

We study the Iwasawa $\lambda$-invariant of Dirichlet characters $\chi$ of arbitrary order for odd primes $p$. From special values of the $p$-adic $L$-function and its derivative we derive several novel and easily computable criteria to distinguish b

Externí odkaz: http://arxiv.org/abs/2401.06100

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On Iwasawa $\lambda$-invariants for abelian number fields and random matrix heuristics

Autor: Delbourgo, Daniel, Knospe, Heiko

Publikováno v: Math. Comp. 92 (2023), 1817-1836

Following both Ernvall-Mets\"{a}nkyl\"{a} and Ellenberg-Jain-Venkatesh, we study the density of the number of zeroes (i.e. the cyclotomic $\lambda$-invariant) for the $p$-adic zeta-function twisted by a Dirichlet character $\chi$ of any order. We are

Externí odkaz: http://arxiv.org/abs/2207.06287

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Dirichlet Series Expansions of p-adic L-Functions

Autor: Knospe, Heiko, Washington, Lawrence C.

We study $p$-adic $L$-functions $L_p(s,\chi)$ for Dirichlet characters $\chi$. We show that $L_p(s,\chi)$ has a Dirichlet series expansion for each regularization parameter $c$ that is prime to $p$ and the conductor of $\chi$. The expansion is proved

Externí odkaz: http://arxiv.org/abs/2102.02851

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A note on regularized Bernoulli distributions and p-adic Dirichlet expansions

Autor: Knospe, Heiko

We consider Bernoulli distributions and their regularizations, which are measures on the $p$-adic integers $\mathbb{Z}_p$. It is well known that their Mellin transform can be used to define $p$-adic $L$-functions. We show that for $p>2$ one of the re

Externí odkaz: http://arxiv.org/abs/2012.15271

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Nonstandard Measure Spaces with Values in non-Archimedean Fields

Autor: Knospe, Heiko

The aim of this contribution is to bring together the areas of $p$-adic analysis and nonstandard analysis. We develop a nonstandard measure theory with values in a complete non-Archimedean valued field $K$, e.g. the $p-$adic numbers $\mathbb{Q}_p$. T

Externí odkaz: http://arxiv.org/abs/1612.09108

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On the Spectrum of Nonstandard Dedekind Rings

Autor: Knospe, Heiko, Serpé, Christian

The methods of nonstandard analysis are applied to algebra and number theory. We study nonstandard Dedekind rings, for example an ultraproduct of the ring of integers of a number field. Such rings possess a rich structure and have interesting relatio

Externí odkaz: http://arxiv.org/abs/1509.06203

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