The specializations of the motivic elliptic polylogarithm on the universal elliptic curve to the modular curve are referred to as Eisenstein classes. In this paper, we prove that the syntomic realization of the Eisenstein classes restricted to the ordinary locus of the modular curve may be expressed using p-adic Eisenstein series of negative weight, which are p-adic modular forms defined using ...

We present the computation modulo p2 and explicit formulas for the unique isogeny covariant differential modular form of order one and weight χ−p−1,−p called fjet, an isogeny covariant differential modular form of order two and weight χ−p2−p,−1,−1 denoted by fjethjet, and an isogeny covariant differential modular form hjet of order two and weight χ1−p2,0,−1.

in this paper, we investigate duality of modular g-riesz bases and g-riesz basesin hilbert c*-modules. first we give some characterization of g-riesz bases in hilbert c*-modules, by using properties of operator theory. next, we characterize the duals of a giveng-riesz basis in hilbert c*-module. in addition, we obtain sucient and necessary conditionfor a dual of a g-riesz basis to be again a g...

MR0004042 (2,309c) 20.0X Brauer, R.; Nesbitt, C. On the modular characters of groups. Annals of Mathematics. Second Series 42 (1941), 556–590. The authors first summarize the theory of modular characters of a finite group G as previously developed by them [Univ. of Toronto Studies, Math. Series, no. 4, 1937]. If an element of G is defined to be p-regular when its order is prime to p, one of the...

An immediate corollary is that it is always possible to pick a Z-lattice inside QS so that the corresponding p-modular reduction is isomorphic to the dual of the conventional p-modular reduction (coming from the standard basis and written FpS λ). Thus our theorem gives a rich source of examples of non-isomorphic p-modular reductions. It would be interesting to know how far it is possible, by pi...

Ming-Lun Hsieh constructed three-variable triple product p-adic L-functions attached to triples of primitive Hida families and proved interpolation formulas. We generalize his result in the unbalanced case construct a L-function family two more general modular forms.

‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

Cryptosystems require the computation of modular exponentiation, this operation is related to the problem of finding a minimal addition chain. However, obtaining the shortest addition chain of length n is an NP-Complete problem whose search space size is proportional to n!. This paper introduces a novel idea to compute the minimal addition chain problem, through an implementation of a Simulated...