Elliptic Functions According to Eisenstein and Kronecker (Google eBook)
Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).
What people are saying - Write a review
We haven't found any reviews in the usual places.
abelian extensions absolutely convergent addition formula algebraic over Q analytic continuation apply assume Chapter character class-numbers coefficients complex multiplier Consequently consider constant terms defined in Chap definition derivatives differential equation Differential Operators differentiated term Dirichlet distribution Eisenstein and Kronecker Eisenstein summation elliptic functions end of Chap entire function expressed factor finite Fourier series functional equation given gives half-plane identity imaginary quadratic fields infinite products introduce Kronecker Kronecker summation L-functions lattice left-hand side lemniscatic Lerch linear meromorphic function notations number-theory observe obtained odd function Partial Differential Pell's equation period-lattice periodic of period Poisson summation pole polynomial power-series proof quadratic form quasicharacter Re(s regarded remains valid replaced residue results of Chap right-hand side s-plane shows simple series substituting summation process summation with respect term by term theorem Theory ISBN theta-series tion transformation formula trigonometric functions verified Weierstrass Werke whole s-plane write written