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Conjecturally, the answer is yes, but the amount of work required is not trivial at all. The general set-up is roughly as follows: the special values of $L$-functions (in your case, for Tate motives) …

Yes, there is. And in surmising correctly that finding a $p$-adic analogue of this formula will provide an understanding of the functional equation of $p$-adic $L$-functions, you have just got a glimp …

The following is more a long comment than an answer per se. One thing to keep in mind when discussing $p$-adic $L$-functions is that to a given algebraic automorphic representation $\pi$ or Galois re …

This question is very simple. Would someone be so nice as to send me an electronic copy of M. M. Vishik, Non-Archimedean measures connected with Dirichlet series, Mat. Sb. (N.S.), 1976, Volume 99( …

Others have hinted at it, but let me emphasize the point. At least if you are happy to assume all conjectures (and perhaps that your motive has good reduction at $p$), the conjectural landscape for $p …

Let $\mathbf{T}$ be the reduced nearly ordinary Hecke algebra of level $N$ of Hida theory for $\operatorname{GL}_{2}$ over $\mathbb{Q}$ (or more generally over a totally real field $F$). Then $\mathbf …

When he introduced $p$-adic numbers, Kurt Hensel produced an incorrect local/global proof of the fact that $e$ is transcendental. Apparently, the intended proof goes along the following lines: studyin …