Let p be a prime number. It’s well known that classical modular Hecke eigenforms can satisfy nontrivial congruence relations modulo powers of p; for example the standard Eisenstein seriesEk satisfiesEp−1 = 1 (mod p), and more generally E(p−1)pr = 1 (mod p) for all integers r ≥ 0. We’d like to construct some kind of p-adic space of modular forms in which this really represents a limiting process...

Our goal will be to generalize the construction of the group Z/nZ. The idea there was to start with the group Z and the subgroup nZ = 〈n〉, where n ∈ N, and to construct a set Z/nZ which then turned out to be a group (under addition) as well. (There are two binary operations + and · on Z, but Z is just a group under addition. Thus, the fact that we can also define multiplication on Z/nZ will not...

We prove a commutative algebra result which has consequences for congruences between automorphic forms modulo prime powers. If C denotes the congruence module for a fixed automorphic Hecke eigenform π0 we prove an exact relation between the p-adic valuation of the order of C and the sum of the exponents of p-power congruences between the Hecke eigenvalues of π0 and other automorphic forms. We a...

Recent research has indicated that operators may utilize the system-wide trust strategy when presented with two automation aids of unknown reliability (Keller, Bean, & Rice, 2009; Keller & Rice, 2010; Keller & Rice, 2009). This is undesirable as operators may under-utilize reliable aids when they are paired with unreliable aids. Two variables derived from Gestalt psychology’s law of similarity ...

We prove the transfer congruence between p-adic Hecke L-functions for CM fields over cyclotomic extensions, which is a non-abelian generalization of the Kummer’s congruence. The ingredients of the proof include the comparison between Hilbert modular varieties, the q-expansion principle, and some modification of Hsieh’s Whittaker model for Katz’ Eisenstein series. As a first application, we prov...

A new combinatorial object is introduced, the part-frequency matrix sequence of a partition, which is elementary to describe and is naturally motivated by Glaisher’s bijection. We prove results that suggest surprising usefulness for such a simple tool, including the existence of a related statistic that realizes every possible Ramanujan-type congruence for the partition function. To further exh...

In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

To every morphism of X∗ a congruence fR on X ∗, called kernel congruence, and defined by ufRv iff f(u) = f(v) can be associated. We characterize morphisms having a commutative kernel congruence and, introducing the notion of the index of a morphism, we give a classification of the morphisms of X∗. Moreover, a congruence with special properties, called hp-congruence is considered; every kernel c...

Background and Purpose: In recent years, studies interest in human behaviour relation to the halal industry have been growing. The process of understanding reasons for planning intention is not an easy path. Intentions are provoked by individual’s attitude which effect on how individuals making per purchase decision (Blackwell, Miniard, & Engel, 2001; Viksne, Salkovska, Gaitniece, Puke, 201...

9 The theory of chi processes with the mismatch operator is studied. Four congruence relations are investigated. These are late open congruence, early open congruence, ground congruence and 11 barbed congruence. The late and early open congruence relations are the chi calculus counterparts of the weak late and early congruence relations of pi calculus. Both turn out to be special cases 13 of th...