English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

He also proved the following similar theorem for prime power cyclotomic fields ([9]): Theorem B. Let n ≥ 1, and let L be the pth cyclotomic field. Put Mn = pn−1(p− 1) max{vp(τ(χ)Lp(1, χ)) : 1 6= χ ∈ Gal(L/Q)∧, even}. Then every unit in L which is congruent to 1 modulo pnpMn−1 n is a pth power of another unit in L, where pn is the unique prime of L above p and τ(χ) is the Gauss sum for χ: τ(χ) = ∑fχ a=1 χ(a)ζ a fχ (fχ is the conductor of χ). Let F be a number field and p a prime. If we assume that Leopoldt’s conjecture is valid for F and p, then there exists an integral ideal M of F whose prime factors are primes above p such that every unit in F which is congruent to 1 modulo M is a pth power of another unit in F . In the present paper, we shall describe this ideal M in terms of the p-adic zeta functions

Kummer's lemma for $ℤ_p$-extensions over totally real number fields