Slopes of Modular Forms
نویسنده
چکیده
Motivation: it would be great if we could understand the p-adic variation of the Up-eigenvalues of modular forms as the weights and/or levels varied. (More generally, it would be really great if we could understand how the local p-adic Galois representations attached to automorphic forms behave – for example, even very weak “equidistribution” results here would presumably imply very strong automorphy lifting theorems. These theorems are only known for GL2 /Q at the moment, and in fact some of the strategies mentioned will go the other way, using those theorems towards equidistribution results.) The discussion below is focused on what little I know about fixing the level and varying the weight. The question of fixing the weight and varying the level is also important, but I know even less about it, barring the connection with automorphy lifting theorems that I will hopefully at least touch on in my talk.
منابع مشابه
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