In his letter (Serre, 1996), J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → Fp, where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms (mod p)...

a $p$-group $g$ is $p$-central if $g^{p}le z(g)$‎, ‎and $g$ is‎ ‎$p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,yin‎ ‎g$‎. ‎we prove that for $g$ a finite $p^{2}$-abelian $p$-central‎ ‎$p$-group‎, ‎excluding certain cases‎, ‎the order of $g$ divides the‎ ‎order of $text{aut}(g)$‎.

Introduction/purpose: The aim of this paper is to present the concept generalized ∅-weak contractive condition involving various combinations d(x,y) in modular metric spaces. Methods: Conventional theoretical methods functional analysis. Results: This study presents result (Murthy & Vara Prasad, 2013) for a single-valued mapping satisfying ∅ -weak d(x,y). It setting spaces, and then it prov...

This note was inspired by a colloquium talk given by S. S. Abhyankar at the Tata Institute, on the work of Abhyankar, Popp and Seiler (see [2]). It was pointed out in this talk that classical modular curves can be used to construct (by specialization) coverings of the affine line in positive characteristic. In this “modular” optic it seemed natural to consider Drinfel’d modular curves for const...