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Search: MSC category 11S80 ( Other analytic theory (analogues of beta and gamma functions, $p$-adic integration, etc.) )

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1. CMB Online first

Otsubo, Noriyuki
Homology of the Fermat tower and universal measures for Jacobi sums
We give a precise description of the homology group of the Fermat curve as a cyclic module over a group ring. As an application, we prove the freeness of the profinite homology of the Fermat tower. This allows us to define measures, an equivalent of Anderson's adelic beta functions, in a similar manner to Ihara's definition of $\ell$-adic universal power series for Jacobi sums. We give a simple proof of the interpolation property using a motivic decomposition of the Fermat curve.

Keywords:Fermat curves, Ihara-Anderson theory, Jacobi sums
Categories:11S80, 11G15, 11R18

2. CMB 2013 (vol 57 pp. 845)

Lei, Antonio
Factorisation of Two-variable $p$-adic $L$-functions
Let $f$ be a modular form which is non-ordinary at $p$. Loeffler has recently constructed four two-variable $p$-adic $L$-functions associated to $f$. In the case where $a_p=0$, he showed that, as in the one-variable case, Pollack's plus and minus splitting applies to these new objects. In this article, we show that such a splitting can be generalised to the case where $a_p\ne0$ using Sprung's logarithmic matrix.

Keywords:modular forms, p-adic L-functions, supersingular primes
Categories:11S40, 11S80

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