Expected Values of Eigenfunction Periods

Expected values in percentile indicators

PP(top x%) is the proportion of papers of a unit (e.g. an institution or a group of researchers), which belongs to the x% most frequently cited papers in the corresponding fields and publication years. It has been proposed that x% of papers can be expected which belongs to the x% most frequently cited papers. In this Letter to the Editor we will present the results of an empirical test whether ...

Periods of Mirrors and Multiple Zeta Values

In a recent paper, A. Libgober showed that the multiplicative sequence {Qi(c1, . . . , ci)} of Chern classes corresponding to the power series Q(z) = Γ(1 + z)−1 appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the periods of their mirrors. We show that the polynomials Qi can be expressed in terms of multiple zeta values. 1. The multiplicative sequence In [6], ...

Multiple Zeta Values and Periods of Moduli

Periods and Special Values of L-functions

Introduction 1 1. Modular forms, congruences and the adjoint L-function 2 2. Quaternion algebras and the Jacquet-Langlands correspondence 6 3. Integral period relations for quaternion algebras over Q 8 4. The theta correspondence 12 5. Arithmetic of the Shimizu lift and Waldspurger’s formula 16 6. Hilbert modular forms, Shimura’s conjecture and a refined version 19 7. Unitary groups and Harris’...

Decomposition of Contingency Table using Expected Values

A contingency table summarizes the conditional frequencies of two attributes and shows how these two attributes are dependent on each other with the information on a partition of universe generated by these attributes. Thus, this table can be viewed as a relation between two attributes with respect to information granularity. This paper focuses on decomposition of a contingency matrix by using ...