some families of mordell curves associated to cubic fields we introduce some mordell curves of two different natures both of which are associated to cubic fields one set of them consists of those elliptic curves whose rational points over the rational number field are described by or closely related to cubic fields the other is a one parameter family of mordell curves which gives all cyclic cubic twists and all quadratic twists of the fermat curve x3 y3 z3 0

a priori bounds for superlinear problems involving the n laplacian abstract in this paper we establish a priori bounds for positive solutions of the equation n u f u u h 0 1 where is a bounded smooth domain in r n and the nonlinearity f has at most exponential growth the techniques used in the proofs are a generalization of the methods of brezis and merle to the n laplacian in combination with the trudinger moser inequality the moving planes method and a comparison principle for the n laplacian

modular elliptic curves and fermat s last theorem when andrew john wiles was 10 years old he read eric temple bell s the last problem and was so impressed by it that he decided that he would be the first person to prove fermat s last theorem this theorem states that there are no nonzero integers a b c n with n 2 such that an bn cn the object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular fermat s last theorem follows as a corollary by virtue of previous work by frey serre and ribet

a certain one parameter additive family of operators defined on analytic functions abstract y komatu proved several interesting results for a certain one parameter additive family of operators defined on analytic functions regular in the unit disk and presented two conjectures for univalent functions in the unit disk it is the purpose of this paper to prove a number of results relevant to komatu s conjectures for certain classes of univalent functions with negative coefficients in the unit disk

some properties of a certain subclass of multivalent analytic functions involving the liu owa operator by making use of the principle of subordination connecting analytic functions and the liu owa operator we introduce a certain subclass of multivalent analytic functions such results as subordination and superordination properties convolution properties distortion theorems inequality properties and sufficient conditions for multivalent starlikeness are proved

on the modularity of elliptic curves over q wild 3 adic exercises in this paper building on work of wiles wi and of wiles and one of us r t tw we will prove the following two theorems see 2 2 theorem a if e q is an elliptic curve then e is modular theorem b if gal q q gl2 f5 is an irreducible continuous representation with cyclotomic determinant then is modular we will first remind the reader of the content of these results and then briefly outline the method of proof if n is a positive integer then we let 1 n denote the subgroup of sl2 z consisting of matrices that modulo n are of the form 1 0 1

inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation let a denote the class of analytic functions with the normalization 0 0 1 0 in the open unit disk u set f l s z z k 2 k l1 l sz k s l 1 z u and define l m s in terms of the hadamard productf l s z f l m s z z 1 z m m 0 z u in this paper the authors introduce several new subclasses of analytic functions defined by means of the operator i l m s a a given byi l m sf z f l m s z f z f a s l 1 m 0 inclusion properties of these classes and the classes involving the generalized libera integral operator are also considered

some functional inequalities and inclusion relationships associated with certain families of integral operators by making use of certain familiar integral operators the authors introduce and investigate several new subclasses of starlike convex close to convex and quasi convex functions among other results presented here the authors establish a number of inclusion relationships associated with some of these integral operators some of the results established in this paper would provide extensions of those given in earlier works

some subclasses of analytic functions associated with fractional calculus operators abstract this paper begins by studying several properties and characteristics of certain subclasses of analytic functions with positive coefficients the results investigated here include various coefficient inequalities distortion properties and the radii of close to convexity inclusion theorems involving the hardy space of analytic functions and the class of functions whose derivative has a positive real part are also investigated relationships between certain subclasses of analytic functions involving fractional derivative operators with negative coefficients and a certain generalized fractional integral operator are then studied various known or new special cases of our results are also pointed out

some further properties of a linear operator associated with the λ generalized hurwitz lerch zeta function related to the class of meromorphically univalent functions in this sequel to the recent work see srivastava 2015 we investigate some further properties of a linear operator associated with srivastava s generalized hurwitz lerch zeta function which are related to a certain class of meromorphically univalent functions in the punctured unit disk defined here by means of the hadamard product or convolution we also give several interesting corollaries and consequences of the main results presented in this paper

majorization problem for certain class of p valently analytic function defined by generalized fractional differintegral operator in this paper we investigate a majorization problem for a subclass of p valently analytic function involving a generalized fractional differintegral operator some useful consequences of the main result are mentioned and relevance with some of the earlier results are also pointed out

some inclusion relationships and integral preserving properties of certain subclasses of meromorphic functions associated with a family of integral operators the object of the present paper is to investigate a family of integral operators defined on the space of normalized meromorphic functions by making use of these novel integral operators we introduce and investigate several new subclasses of starlike convex close to convex and quasi convex meromorphic functions in particular we establish some inclusion relationships associated with the aforementioned integral operators several interesting integral preserving properties are also considered

the hardy space of analytic functions associated with certain one parameter families of integral operators abstract recently h m srivastava and s owa j math anal appl 118 1986 80 87 proved a number of results relevant to komatu s conjectures cf y komatu bull fac sci engrg chuo univ ser i math 22 1979 1 22 for a certain one parameter additive family of operators defined on analytic functions regular in the open unit disk the object of the present paper is to investigate several one parameter families of integral operators and to prove certain inclusion theorems involving the hardy space h p of analytic functions and the class of functions whose derivative has a positive real part an application involving a generalized hypergeometric function is also considered

uniform bounds for higher order semilinear problems in conformal dimension abstract we establish uniform a priori estimates for solutions of the semilinear dirichlet problem m u h x u in u n u n m 1 u 0 on where h is a positive superlinear and subcritical nonlinearity in the sense of the trudinger moser adams inequality either when is a ball or provided an energy control on solutions is prescribed when is a smooth bounded domain our results are sharp within the class of distributional solutions the analogous problem with navier boundary conditions is also studied finally as a consequence of our results existence of a positive solution is shown by degree theory

an application of certain integral operators the integral operator i n f z was introduced by salagean for func tions of the form f z z 1 p k 2 a kz k which are analytic in the unit disc

properties for uniformly starlike and related functions under the srivastava attiya operator abstract in the present paper we introduce and investigate classes of analytic functions involving the srivastava attiya operator basic properties for uniformly starlike functions of order are studied such as inclusion relations sufficient conditions coefficient inequalities and distortion inequalities the results are also extended to uniformly convex close to convex and quasi convex functions relevant connections of the results presented here with those obtained in earlier works are also pointed out

a priori estimates and existence for elliptic systems via bootstrap in weighted lebesgue spaces we present a new general method to obtain regularity and a priori estimates for solutions of semilinear elliptic systems in bounded domains this method is based on a bootstrap procedure used alternatively on each component in the scale of weighted lebesgue spaces lp lp x dx where x is the distance to the boundary using this method we significantly improve the known existence results for various classes of elliptic systems

applications of certain operators to the classes of analytic functions related with generalized conic domains let a be the class of functions f f z z n 2 a nz n which are analytic in the open unit disc e we use a linear operator closely related to the multiplier transformation to introduce and investigate certain subclasses of a which map e onto a generalized form of the conic domain several properties of these classes including some inclusion relations convolution and other class preserving operators are studied in particular we derive many known and new results as special cases applications of some results are also given

classes of functions defined by certain differential integral operators abstract in this paper we investigate a class of p valent analytic functions with fixed argument of coefficient which is defined in terms of certain differential integral operators coefficient estimates distortion theorems extreme points the radii of convexity and starlikeness in this class are given

sandwich type theorems for multivalent functions associated with the srivastava attiya operator abstract in the present paper we investigate some subordination and superordination preserving properties for certain classes of analytic and multivalent functions in the open unit disk which are associated with such multiplier transformations as the srivastava attiya operator various sandwich type theorems for functions belonging to these classes are also obtained

some preserving subordination and superordination of analytic functions involving the liu owa integral operator in this paper we obtain some subordination and superordination preserving results of analytic functions involving the liu owa integral operator sandwich type result is also obtained

a unified class of analytic functions involving a generalization of the srivastava attiya operator in this paper we present a unified class of analytic functions defined by a new convolution operator j p q b s a introduced recently by srivastava and gaboury 2014 which generalizes the well known srivastava attiya operator investigated by srivastava and attiya 2007 we derive coefficient inequalities growth and distortion theorems extreme points and fekete szego problem for this new function class

notes on jung kim srivastava integral operator abstract the object of the present paper is to investigate some properties of certain integral operator q introduced and studied recently by jung kim and srivastava j math anal appl 176 1993 138 147