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Zeta and $L$-functions in Number Theory and Combinatorics

Wen-Ching Winnie Li Pennsylvania State University, University Park, PA
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-1-4704-4900-1
Product Code: CBMS/129
List Price: $55.00 MAA Member Price:$49.50
AMS Member Price: $44.00 Electronic ISBN: 978-1-4704-5192-9 Product Code: CBMS/129.E List Price:$55.00
MAA Member Price: $49.50 AMS Member Price:$44.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $82.50 MAA Member Price:$74.25
AMS Member Price: $66.00 Click above image for expanded view Zeta and$L$-functions in Number Theory and Combinatorics Wen-Ching Winnie Li Pennsylvania State University, University Park, PA A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-1-4704-4900-1 Product Code: CBMS/129  List Price:$55.00 MAA Member Price: $49.50 AMS Member Price:$44.00
 Electronic ISBN: 978-1-4704-5192-9 Product Code: CBMS/129.E
 List Price: $55.00 MAA Member Price:$49.50 AMS Member Price: $44.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$82.50 MAA Member Price: $74.25 AMS Member Price:$66.00
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1292019; 95 pp
MSC: Primary 11; 05;

Zeta and $L$-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and $L$-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem.

The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented.

Research on zeta and $L$-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

Graduate students and researchers interested in Zeta and $L$-functions.

• Chapters
• Number theoretic zeta and $L$-functions
• The Selberg zeta function
• $L$-functions in geometry
• The Ihara zeta function
• Spectral graph theory
• Explicit constructions of Ramanujan graphs
• Artin $L$-functions and prime distributions for graphs
• Zeta and $L$-functions of complexes

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 1292019; 95 pp
MSC: Primary 11; 05;

Zeta and $L$-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and $L$-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem.

The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented.

Research on zeta and $L$-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

Graduate students and researchers interested in Zeta and $L$-functions.

• Chapters
• Number theoretic zeta and $L$-functions
• The Selberg zeta function
• $L$-functions in geometry
• The Ihara zeta function
• Spectral graph theory
• Explicit constructions of Ramanujan graphs
• Artin $L$-functions and prime distributions for graphs
• Zeta and $L$-functions of complexes
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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