Modular functions and dirichlet series in number theory

Undergraduate texts in mathematics evolved from a course mathematics 160 offered at the california institute of technology during the last 25 years. Most of the present volume is devoted to elliptic functions and modular functions with some of their numbertheoretic applications. Most of the present volume is devoted to elliptic functions and modular functions with some of. First volume of a twovolume textbook which evolved from a course mathematics 160 offered at the california institute of technology and continued by the authors modular functions and dirichlet series in number theory includes index bibliography. This is the second volume of a 2volume textbook which evolved from a course mathematics 160 offered at the california institute of technology during the. Download modular functions and dirichlet series in number theory in pdf and epub formats for free. Modular functions and dirichlet series in number theory book. Question 6th of apostol modular functions and dirichlet. Tom m apostol this volume is a sequel to the authors introduction to analytic.

For any complex number with, let, then the eta function is defined by. A new edition of a classical treatment of elliptic and modular functions with some of their numbertheoretic applications, this text offers an updated bibliography. An extended generalized q extensions for the apostol type polynomials castilla. Among the major topics treated are rademachers convergent series for the partition function, lehners congruences for the fourier coefficients of the modular function jtau, and heckes theory of entire forms. Modular functions and dirichlet series in number theory tom m. Modular functions and dirichlet series in number theory graduate. Modular functions and dirichlet series in number theory pdf free. Springer monographs in mathematics goro shimura eelementary dirichlet series and modular forms goro shimura depar. Modular functions and dirichlet series in number theory by marvin isadore knopp. Topics include arithmetic functions, dirichlet characters, gauss and character sums, summation formulae, lfunctions and associated properties, primes in arithmetic. Modular functions and dirichlet series in number theory has 3 available editions to buy at half price books marketplace. A new edition of a classical treatment of elliptic and modular functions with some of their number theoretic applications, this text offers an updated bibliography.

Modular functions and dirichlet series in number theory is, technically, the second volume of apostols introduction to analytic number theory. Kop modular functions and dirichlet series in number theory av tom m apostol pa. The presence of 24 can be understood by connection with. This volume is a sequel to the authors introduction to analytic number theory utm 1976, 3rd printing 1986. Among the major topics treated are rademachers convergent series for the partition function, lehners congruences for the fourier coefficients of the modular functionj r, and heckes theory of entire forms with multiplicative fourier coefficients. Modular functions and dirichlet series in number theory by. Zagier the modular group takes its name from the fact that the points of the quotient space. Uncommonly good collectible and rare books from uncommonly good booksellers. Modular functions and dirichlet series in number theory by tom m. Modular functions and dirichlet series in number theory topic outline.

Among the major topics treated are rademachers convergent series for the partition function, lehners congruences for the fourier coefficients of the modular functionj r, and heckes theory of entire forms with. Among the major topics treated are rademachers convergent series for the partition function, lehners congruences for the. This course provides students with a solid working knowledge in the fundamentals of analytic number theory. First volume of a twovolume textbook which evolved from a course mathematics 160 offered at the california institute of technology and continued by the authors modular functions and dirichlet series in number theory. Modular functions and dirichlet series in number theory graduate texts in mathematics. In mathematics, in the area of analytic number theory, the dirichlet eta function is defined by the following dirichlet series, which converges for any complex number having real part 0. Publication date 1990 topics functions, elliptic, functions, modular, number theory, series, dirichlet publisher.

In mathematics, the dedekind eta function, named after richard dedekind, is a modular form of weight 12 and is a function defined on the upper halfplane of complex numbers, where the imaginary part is positive. The first volume appeared in springers undergraduate texts in mathematics series, and i have written a very positive. On potential automorphy, and other topics in number theory, phd thesis, thomas barnetlamb, harvard university 2009 on euclidean ideal classes, phd thesis, hester k. According to martin eichler, there are five fundamental operations of mathematics. Apostol, 9780387971278, available at book depository with free delivery worldwide. Tom m apostol this volume is a sequel to the authors introduction to analytic number theory utm 1976, 3rd printing 1986. Since then, the hecke correspondence has remained an active feature of number theory and, indeed, it is more important today than it was in 1936. Modular functions and dirichlet series in number theory scribd. Buy modular functions and dirichlet series in number theory graduate texts in mathematics 2nd ed.

Tom m apostol this is the second volume of a 2volume textbook which evolved from a course mathematics 160 offered at the california institute of technology du ring the last 25 years. Both volumes grew out of the notes for a course that apostol had already offered at caltech for over 25. Apostol t modular functions and dirichlet series in. Find modular functions and dirichlet series in number theory by apostol, tom m at biblio. Regarding proving a series result from tom m apostol modular functions and dirichlet series in number theory 2 doubt in exercise 3. Apostol a new edition of a classical treatment of elliptic and modular functions with some of their numbertheoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the dedekind eta function.

Apostol this volume is a sequel to the authors introduction to analytic number theory utm 1976, 3rd printing 1986. The volume presupposes a background in number theory comparable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Modular functions and dirichlet series in number theory book, 1990. Modular functions and dirichlet series in number theory has 3 available editions. Among the major topics treated are rademachers convergent series for the partition function, lehners congruences for the fourier coefficients of the modular functionjr, and heckes theory of entire forms with. This dirichlet series is the alternating sum corresponding to the dirichlet series expansion of the riemann zeta function. Most of the present volume is devoted to elliptic functions and modular functions with some of their number theoretic applications. This is an introduction to the arithmetic theory of modular functions and modular forms, with a greater emphasis on the geometry than most accounts. Modular functions and dirichlet series in number theory by apostol, tom m.

Modular functions and dirichlet series in number theory. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Everyday low prices and free delivery on eligible orders. Buy modular functions and dirichlet series in number theory graduate texts in mathematics 41 v. Buy modular functions and dirichlet series in number theory. In 1938, at the institute for advanced study, e hecke gave a series of lectures on his theory of correspondence between modular forms and dirichlet series. Enter your mobile number or email address below and well send you a link to download the free kindle app.

Buy modular functions and dirichlet series in number theory graduate texts in mathematics book online at best prices in india on. Partition function number theory integer partition. It presupposes an undergraduate background in number theory comparable to that provided. Heckes theory of modular forms and dirichlet series.

Modular functions and modular forms elliptic modular curves j. Heckes theory of modular forms and dirichlet series will be of huge importance to fledgling number theorists working on modular forms in fact, given heckes exalted place in this part of the firmament, the book is really indispensable. This is a list of number theory topics, by wikipedia page. Multiplicative number theory building on its broad strengths in mathematics in general, and in special functions in particular, the wolfram language provides a unique level of support for multiplicative number theory, including not only highly general function evaluation, but also symbolic simplification. Rankincohen brackets on hilbert modular forms and special values of certain dirichlet series kumari, moni and sahu, brundaban, functiones et approximatio commentarii mathematici, 2018.

Apostol, modular functions and dirichlet series in number theory. Apostol t modular functions and dirichlet series in number theory 0387971270 free ebook download as pdf file. Congruences for the coefficients of the modular function j. Building on its broad strengths in mathematics in general, and in special functions in particular, the wolfram language provides a unique level of support for multiplicative number theory, including not only highly general function evaluation, but also symbolic simplification. Buy a cheap copy of modular functions and dirichlet series. Raising the eta equation to the 24th power and multiplying by 2. Apostol a new edition of a classical treatment of elliptic and modular functions with some of their number theoretic applications, this text offers an updated bibliography and an alternative treatment of the transformation formula for the dedekind eta function. Definition in terms of lattices or elliptic curves. Dec 06, 2012 the second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. A modular form can equivalently be defined as a function f from the set of lattices in c to the set of complex numbers which satisfies certain conditions. Modular functions and dirichlet series in number theory graduate texts in mathematics 41 v.