A Brief Introduction to Theta Functions (Dover Books on Mathematics) by Richard Bellman (PDF)

Description

Brief but intriguing, this monograph on the theory of elliptic functions was written by one of America’s most prominent and widely read mathematicians. Richard Bellman encompasses a wealth of material in a succession of short chapters, spotlighting high points of the fundamental regions of elliptic functions and illustrating powerful and versatile analytic methods. Suitable for advanced undergraduates and graduate students in mathematics, this introductory treatment is largely self-contained. Topics include Fourier series, sufficient conditions, the Laplace transform, results of Doetsch and Kober-Erdelyi, Gaussian sums, and Euler’s formulas and functional equations. Additional subjects include partial fractions, mock theta functions, Hermite’s method, convergence proof, elementary functional relations, multidimensional Poisson summation formula, the modular transformation, and many other areas.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Great text on the theta function.

⭐I first chanced upon Richard Bellman’s wonderful little book in a library nearly 40 years ago, and have been looking for an affordable copy ever since. Many thanks to Dover for at last coming up with this reprint!The book is dedicated ‘to devotees of analytic number theory’, and does require a basic knowledge of complex-variable theory, at the level of a first degree in mathematics. With that background (now pretty rusty, in my case), I had little difficulty following Bellman’s clear exposition as he rapidly canters through the derivation of numerous beautiful – and some startling – results involving theta functions. His emphasis is on vigour, rather than on rigour: copious references are given to the original papers for more detailed treatments.As a lover of elegant formulae, I shared Lame’s goose-bumps (see page 48) on seeing many of the equations, though I cannot approach G. N. Watson’s eloquence on the same page…A minor complaint – it is a pity that Dover didn’t take the opportunity of eliminating a few errors that were present in the original edition. For example, on page 16 a missing equation 12.3 is referred to (though it is easy to reconstruct); strangely, an error in equation (12.4) on the same page has apparently been corrected by hand. The title to Section 11 refers to Modular Functions, although these are not defined; they are presumably the same as the ‘automorphic functions’ defined in equation (11.8).But these little blemishes do not seriously detract from a gem of a book, which can profitably be dipped into, time after time.

⭐This brief introduction to Theta functions delivers on its promise. The exposition is right to the point and very helpful. Hignly recommended.

⭐Trata-se de uma exposição breve e didática de um tema não muito usual na disciplina de física matemática. Recomendo fortemente a sua leitura para os estudantes de física teórica.

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⭐Ottima introduzione alle proprieta` delle funzioni teta.

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⭐no puedo opinar, me censuran los censores de amazon.es

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