Titlebook: Current Trends in Number Theory; Sukumar Das Adhikari,Shashikant A. Katre,B. Ramakr Book 2002 Hindustan Book Agency (India) 2002

motivate

On Automorphism Groups of Algebraic Curves, we give classical results on the upper bounds of the order of Aut(.). In §2, we discuss the relation between Aut(.) and .-ranks of ., when the ground field . has characteristic . > 0. Finally in §3, we give an upper bound of the orders of abelian subgroups of Aut(.).

PON

Zeta Functions for Curves Defined over Finite Fields,lds. We state these conjectures, and also the more recent Weil theorem for singular curves defined over finite fields. We end by remarking on some explicit results we have obtained for the zeta functions of some concrete classes of curves (both non-singular and singular) defined over a certain class

ethnology

Occlusion

Some Aspects of the Central Critical Value of Automorphic ,-functions,tivity, algebraicity, growth properties with respect to naturally attached parameters etc. In this expository article we will briefly describe some of those developments for a special class of automorphic .-functions which will be introduced below. Our aim is to provide the reader a glimpse of this

創(chuàng)作

Integral Points on the Circle , + , = ,questions. . Note that (±1,0) and (0, ±1) are trivial integral solutions of (1). If . denotes the set of all . satisfying (1), then . is an abelian group under the composition,.In [PS1], we proved the following theorem, which determines the structure of this group in terms of the number of complex i

Rinne-Test

An Equation of Goormaghtigh and Diophantine Approximations, can be viewed as updating Section 3 of [26]. Further, we shall consider an extension of (1) with . = 3 and derive a new result from a recent theorem of Bilu, Hanrot and Voutier [4] on primitive divisors of Lucas and Lehmer sequences. We shall also discuss some general results on diophantine approxi

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