On the arithmetic of fibered surfaces

Kaba, Mustafa Devrim
In the first three chapters of this thesis we study two conjectures relating arithmetic with geometry, namely Tate and Lang’s conjectures, for a certain class of algebraic surfaces. The surfaces we are interested in are assumed to be defined over a number field, have irregularity two and admit a genus two fibration over an elliptic curve. In the final chapter of the thesis we prove the isomorphism of the Picard motives of an arbitrary variety and its Albanese variety.


On the Krall-type polynomials on q-quadratic lattices
Alvarez-Nodarse, R.; Adiguzel, R. Sevinik (Elsevier BV, 2011-08-01)
In this paper, we study the Krall-type polynomials on non-uniform lattices. For these polynomials the second order linear difference equation, q-basic series representation and three-term recurrence relations are obtained. In particular, the q-Racah-Krall polynomials obtained via the addition of two mass points to the weight function of the non-standard q-Racah polynomials at the ends of the interval of orthogonality are considered in detail. Some important limit cases are also discussed. (C) 2011 Royal Net...
Qualitative behavior of solutions of dynamic equations on time scales
Mert, Raziye; Ağacık, Zafer; Department of Mathematics (2010)
In this thesis, the asymptotic behavior and oscillation of solutions of dynamic equations on time scales are studied. In the first part of the thesis, asymptotic equivalence and asymptotic equilibrium of dynamic systems are investigated. Sufficient conditions are established for the asymptotic equivalence of linear systems and linear and quasilinear systems, respectively, and for the asymptotic equilibrium of quasilinear systems by unifying and extending some known results for differential systems and diffe...
BASKAL, S; ERIS, A; SATIR, A (1994-12-19)
The symmetries and associated conservation laws of the SO(2,1) invariant non-linear sigma model equations in 1+1 dimensions are investigated. An infinite family of generalized local symmetries is presented and the uniqueness of these solutions is discussed.
On the arithmetic operations over finite fields of characteristic three with low complexity
AKLEYLEK, SEDAT; Özbudak, Ferruh; Özel, Claire Susanna (2014-03-15)
In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F-3n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard p...
Proof of the basic theorem on concept lattices in Isabelle/HOL
Sertkaya, B; Oğuztüzün, Mehmet Halit S. (2004-01-01)
This paper presents a machine-checked proof of the Basic Theorem on Concept Lattices, which appears in the book "Formal Concept Analysis" by Canter and Wille, in the Isabelle/HOL Proof Assistant. As a by-product, the underlying lattice theory by Kammueller has been extended.
Citation Formats
M. D. Kaba, “On the arithmetic of fibered surfaces,” Ph.D. - Doctoral Program, Middle East Technical University, 2011.