On computation of basis of $p$-adic logarithmMabud Ali SarkarAbsos Ali Shaikh
The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gam...
The quantity Rp(k) is defined just as R(k) but with the Iwasawa p-adic logarithm replacing the usual logarithm. Note that the terms Rp(k) and dk are only defined up to a sign, but Rp(k)/dk can be defined without ambiguity. It is known that Rp(k) is non-zero for abelian ...
Bertolini-Darmon and Mok proved a formula of the second derivative of the two-variable p p p -adic L L L -function of a modular elliptic curve over a totally real field along the Hida family in terms of the image of a global point by some p p p -adic logarithm map. The theory ...
I wonder which prime numbers pp are such that lim supn→+∞νp(an)=+∞lim supn→+∞νp(an)=+∞, where νpνp denotes the pp-adic valuation. It is not enough for pp to divide one of the terms of the sequence aa: indeed 13∣a513∣a5 but no term of the sequence aa...
104.1 The p-adic elliptic logarithm The formal group of an elliptic curve E arises from expanding everything associated to E (the Weierstrass equation, the coordinate functions, the group la...Satoh, T., Araki, K.: Fermat quotients... Satoh,Takakazu,Araki,... - 《Commentarii Mathematici Uni...
We shall designate by log thep-adic logarithm defined by the usual series A Brumer - 《Mathematika》 被引量: 310发表: 1967年 Wave function of the universe and p-adic gravity A new approach to the wave function of the universe is suggested. The key idea is to take into account ...
The restriction of the p-adic logarithm gives a homomorphism \begin{aligned} \log _{\omega _{B_{f}}}: B_{f}(\mathcal {H}_{\chi }) \rightarrow \mathbf {C}_{p}. \end{aligned} We extend it to B_{f}(\mathcal {H}_{\chi }) \otimes _{\mathcal O_{\mathcal {E}_{f...
The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic ...
We prove formulas for the p-adic logarithm of quaternionic Darmon points on p-adic tori and modular abelian varieties over Q having purely multiplicative reduction at p. These formulas are amenable to explicit computations and are the first to treat Stark-Heegner type points on higher-dimensional...