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## Details

Genre/Form: | Popular works |
---|---|

Document Type: | Book |

All Authors / Contributors: |
Avner Ash; Robert Gross |

ISBN: | 9780691170190 0691170193 |

OCLC Number: | 1001699559 |

Description: | xiv, [4], 220 s. : illustrations |

Contents: | PART ONE. FINITE SUMS -- 1. Proem -- 2. Sums of two squares -- 3. Sums of three and four squares -- 4. Sums of higher powers: waring's problem -- 5. Simple sums -- 6. Sums of powers, using lots of algebra -- PART TWO. INFINITE SUMS -- 7. Infinite series -- 8. Cast of characters -- 9. Zeta and Bernoulli -- 10. Count the ways -- PART III. MODULAR FORMS AND THEIR APPLICATIONS -- 11. The upper half-plane -- 12. Modular forms -- 13. How many modular forms are there? -- 14. Congruence groups -- 15. Partitions and sums of squares revisited -- 16. More theory of modular forms -- 17. More things to do with modular forms: applications. |

Responsibility: | Avner Ash and Robert Gross. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"Offers a clear and beautiful progression from addition to modern number theory."--Math-Blog "The authors did a remarkable job in making some aspects of modern number theory very accessible to readers with only a minimal knowledge of mathematics, say a student who had a first calculus course. However, also mathematicians who do not have number theory as their main focus will enjoy this book."--Adhemar Bultheel, European Mathematical Society "Ash and Gross do a masterful job of leading students from finite sums to modular forms and to the forefront of modern number theory... This is an excellent piece of mathematical writing."--Choice "[A]n accessible and fun introduction to modular forms... [Summing It Up] is engaging and conversational, without losing accuracy or essential rigor."--Dominic Lanphier, American Mathematical Monthly Read more...

*User-contributed reviews*