Unit L-Functions and a Conjecture of Katz

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi–Yau threefold in P provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces.

a contrastive study of rhetorical functions of citation in iranian and international elt scopus journals

writing an academic article requires the researchers to provide support for their works by learning how to cite the works of others. various studies regarding the analysis of citation in m.a theses have been done, while little work has been done on comparison of citations among elt scopus journal articles, and so the dearth of research in this area demands for further investigation into citatio...

Dwork's Conjecture 1 Dwork's Conjecture on Unit Root Zeta Functions

A Symplectic Test of the L-Functions Ratios Conjecture

Recently Conrey, Farmer and Zirnbauer [CFZ1, CFZ2] conjectured formulas for the averages over a family of ratios of products of shifted L-functions. Their L-functions Ratios Conjecture predicts both the main and lower order terms for many problems, ranging from n-level correlations and densities to mollifiers and moments to vanishing at the central point. There are now many results showing agre...

Rigidity, locally symmetric varieties and the Grothendieck-Katz Conjecture

Using Margulis’s results on lattices in semisimple Lie groups, we prove the GrothendieckKatz p-Curvature Conjecture for many locally symmetric varieties, including HilbertBlumenthal modular varieties and the moduli space of abelian varieties Ag when g > 1.