Let K be a global field of char p and let Fq be the algebraic closure of Fp in K. For an elliptic curve E/K with non-constant j-invariant, the L-function L(T,E/K) is a polynomial in 1+T ·Z[T ]. For any N > 1 invertible in K and finite subgroup T ⊂ E(K) of order N , we compute the mod N reduction of L(T,E/K) and determine an upper-bound for the order of vanishing at 1/q, the so-called analytic r...

Let F be an algebraic number field. Recently, L. Weng introduced zeta functions of rank n associated to F as a generalization of the Iwasawa-Tate zeta integral from the Arakelov geometric point of view. In the article, we call them the Weng zeta function of rank n. In the case of rank one, the Weng zeta function coincide with the Dedekind zeta function of F . The background and precise definiti...

1. Introduction In the higher rank paper 17], we reduced Dwork's conjecture from higher rank case over any smooth aane variety X to the rank one case over the simplest aane space A n. In the present paper, we nish our proof by proving the rank one case of Dwork's conjecture over the aane space A n , which is called the key lemma in 17]. The key lemma had already been proved in 16] in the specia...

We explore the effect of zeros at the central point on nearby zeros of elliptic curve L-functions, especially for one-parameter families of rank r over Q. By the Birch and Swinnerton Dyer Conjecture and Silverman’s Specialization Theorem, for t sufficiently large the L-function of each curve Et in the family has r zeros (called the family zeros) at the central point. We observe experimentally a...

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

Sufficient and necessary results have been proven on Lipschitz type integral conditions bounds of its Fourier transform for an $L^2$ function, in the setting Riemannian symmetric spaces rank $1$ whose growth depends a $k$th-order modulus continuity.