1. CMB 2016 (vol 59 pp. 624)
||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)
||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
Keywords:modular forms, p-adic L-functions, supersingular primes