Note on the modular forms

A note on modular forms and generalized anomaly cancellation formulas

By studying modular invariance properties of some characteristic forms, we prove some new anomaly cancellation formulas which generalize the Han-Zhang and Han-Liu-Zhang anomaly cancellation formulas

A note on modular hyperconvex space

a note on modular hyperconvex space

Modular Forms on

Let k 2 Z and let SL 2 (Z) denote the special linear group SL 2 (Z) = a b c d : a; b; c; d 2 Z and ad bc = 1 : A modular form of weight k is an analytic function f de…ned on the complex upper half plane H = fz 2 C : Im(z) > 0g that transforms under the action of SL 2 (Z) according to the relation [1] f az + b cz + d = (cz + d) k f (z) for all a b c d 2 SL 2 (Z)

A note on the p-adic Galois representations attached to Hilbert modular forms

We show that the p-adic Galois representations attached to Hilbert modular forms of motivic weight are potentially semistable at all places above p and are compatible with the local Langlands correspondence at these places, proving this for those forms not covered by the previous works of T. Saito and of D. Blasius and J. Rogawski. 2000 Mathematics Subject Classification: 11F80, 11F41