Hidetaka Kitayama

ON THE GRADED RING OF SIEGEL MODULAR FORMS OF DEGREE TWO WITH RESPECT TO A NON-SPLIT SYMPLECTIC GROUP

We will give an explicit ring structure of the graded ring of Siegel modular forms of degree two with respect to a certain discrete subgroup of Sp(2;ℝ) contained in a non-split ℚ-form. We will also give the fundamental relations among the generators.

On the irreducibility of Fibonacci and Lucas polynomials over finite fields

Abstract In this paper, we give the necessary and sufficient condition that Fibonacci and Lucas polynomials are irreducible in F q [ T ] . As applications of our results, under the GRH, we prove that there are infinitely many irreducible Fibonacci and Lucas polynomials in F q [ T ] for some q.

On Explicit Dimension Formulas for Spaces of Siegel Cusp Forms of Degree Two and Their Applications

In this article, we will survey our studies of explicit dimension formulas for Siegel cusp forms of degree two and their applications. After we summarize some known results in Sect. 3, we will explain a new result which was obtained in a joint work with Ibukiyama. It is an explicit dimension formula for Siegel paramodular cusp forms of square-free level. We will discuss its application in Sect. 5.