In this paper we studied the symmetries of standard electromagnetic action. First, we obtained two identities to calculate energy-momentum tensor directly from transformation symmetry without manually inserting any divergence-free terms. Then we fou…

Throughout the proof, all the assumptions of Theorem (1.3) are in force. Without loss of generality, and for notational convenience, it is assumed that ¯¯¯P=P∞. Then, with Zn:=(dPn/d¯¯¯P)|¯¯¯F for all n∈N∪{∞}, ¯¯¯P-limn→∞ZnT=1=Z∞T holds for all T∈R+.

Theorem 4.2.4 implies that the mod p differential operators from Section 3 map Hecke eigenforms to Hecke eigenforms. When there are Galois representations arising from the corresponding systems of Hecke eigenvalues, it is natural to ask how our diff…