We use cookies to make your experience better. By continuing to browse our site you are agreeing to our use of cookies. Learn more.
Exponential Sums, Hypergeometric Sheaves, and Monodromy Groups (Book 220) by Nicholas M. Katz
£62.00
Available
Product Ref. (e.g. ISBN, SKU)
9780691272252
Published:
24 Jun 2025
Format:
Paperback
Number of pages:
594 pages
Dimensions:
234.95x155.57mm
Weight:
0.000kgs
Author:
Book 220 from the Annals of mathematics studies series.
This is an examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields.
An examination of some of the remarkable connections between group theory and arithmetic algebraic geometry over finite fields
Exponential sums have been of great interest ever since Gauss, and their importance in analytic number theory goes back a century to Kloosterman. Grothendieck's creation of the machinery of l-adic cohomology led to the understanding that families of exponential sums give rise to local systems, while Deligne, who gave his general equidistribution theorem after proving the Riemann hypothesis part of the Weil conjectures, established the importance of the monodromy groups of these local systems. Deligne's theorem shows that the monodromy group of the local system incarnating a given family of exponential sums determines key statistical properties of the family of exponential sums in question. Despite the apparent simplicity of this relation of monodromy groups to statistical properties, the actual determination of the monodromy group in any particular situation is highly nontrivial and leads to many interesting questions.
This book is devoted to the determination of the monodromy groups attached to various explicit families of exponential sums, especially those attached to hypergeometric sheaves, arguably the simplest local systems on G_m, and to some simple (in the sense of simple to write down) one-parameter families of one-variable sums. These last families turn out to have surprising connections to hypergeometric sheaves. One of the main technical advances of this book is to bring to bear a group-theoretic condition (S+), which, when it applies, implies very strong structural constraints on the monodromy group, and to show that (S+) does indeed apply to the monodromy groups of most hypergeometric sheaves.
About the Author: Nicholas M. Katz is professor of mathematics at Princeton University. His books include Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (Princeton). Pham Huu Tiep is the Joshua Barlaz Professor and Distinguished Professor of Mathematics at Rutgers University.
| Number of pages | 594 |
|---|
We will despatch your order as quickly as we can. If, for whatever reason, a product is out of stock we will contact you to discuss the likely delivery time or an alternative product.
| First Item | 2 Items & Over | |
|---|---|---|
| UK | £3.75 | £5.00 |
| EU | £15.00 | £30.00 |
| USA & Canada | £30.00 | £50.00 |
| Rest of the World | £45.00 | £60.00 |
| Collect in Store | free | free |
Additional Delivery Information (and some really important bits):
UK Delivery
Orders for delivery in the UK are normally despatched by Royal Mail, using the RM 48 Tracked Service with most orders delivered to you within a few days of placing your order with us. For larger parcels, Courier and Signed For delivery services may be used. Signed Books are shipped in our specially made book mailing cartons, with the books themselves wrapped in paper to protect them. Sometimes we may ship your order in several parts, particularly if you have 'Pre-Order' titles in your order or titles which are held in stock with our publishing partners.
The Really Important Bit: Because we use tracked, courier and signed for delivery services, please use an address at which your parcel can be received during the normal working day, for example, you may want to have your order delivered to your work address if you're not at home during the day.
First Item @ £3.75 (sometimes a shipping supplement may be added for particularly heavy books or specific postcodes*)
2 Items & over @ £5.00 in total
Another Really Important Bit: There are a number of Postcodes in the UK for which we will need to charge a shipping supplement, this will be calculated once we know the size and weight of the shipment. For these orders we will contact customers to agree a suitable and economic method of shipping. There may also be additional time required for delivery to some areas of the United Kingdom. Where possible, we will ship book orders (under 2kg) by Royal Mail to all UK postcodes. Large multiple book orders and books over 2kg are often shipped via APC Overnight or similar, regardless of Postcode.
Overseas Delivery
Shipments to EU countries:
First Item @ £15.00 (sometimes a shipping supplement will be added for particularly heavy books)
2 Items & over @ £30.00 in total
A really, really important Brexit bit: From 1st January 2021 shipments to EU addresses may incur additional costs which could be requested by Fed Ex at the time of delivery. These costs may vary from country to country and are not within our control and will be in addition to the costs paid to us for your delivery. If in any doubt, please check with your local Fed Ex office what, if any, additional costs will be applicable to your order - https://www.fedex.com
From 1st July 2021, VAT will be applicable to those EU countries where VAT is applied to books - this additional charge will be collected by Fed Ex (or the Royal Mail) at the time of delivery.
Shipments to the USA & Canada:
First Item @ £30.00
2 Items & over @ £50.00 in total
Shipments to the Rest of the World:
First Item @ £45.00
2 Items & over @ £60.00 in total
All overseas orders are shipped using a 'signed for' courier service - please provide an address at which your parcel can be signed for on receipt. We use the same packaging materials for our overseas deliveries as we do those in the UK. In some cases, particularly large and heavy books, or books being shipped to remote areas, may incur an additional shipping charge - if this is the case with your order, we'll notify you as quickly as possible of these charges and to arrange the additional payment. You can of course cancel your order with an immediate refund should you not wish to accept these additional costs. Shipments to overseas territories may incur additional Duty & Tax costs which could be requested by Fed Ex at the time of delivery. These costs may vary from country to country and are not within our control and will be in addition to the costs paid to us for your delivery. If in any doubt, please check with your local Fed Ex office what, if any, additional Tax & Duty costs will be applicable to your order - https://www.fedex.com
Collect in Person at Coles Books
We're open Monday - Saturday, 9:00am - 5:30pm. If you're collecting your order, please wait until you get the text, phone call or email from us, just to be on the safe side and to ensure we have your order ready for you on arrival (we'll use the contact information provided during checkout). Not everything on our website is available for immediate collection, please do wait for the text, call or email - if time is of the essence, we'd suggest you call us on 01869 320779 and check availability prior to placing your order. You can pick up your order from the till, please bring a copy of your email receipt (electronic or printed is fine).
Coming by Car
If you're coming to Coles by car, why not take advantage of the 2 hours free parking at Sainsbury's Pioneer Square - just follow the signs for Pioneer Square as you drive into Bicester and park in the multi-storey car park above the supermarket. Come down the travelators, exit Sainsbury's, turn right and follow the pedestrianised walkway to Crown Walk and turn right - and Coles will be right in front of you. You don't need to shop in Sainsbury's to get the free parking!
Where to Find Us
Coles Books
22 Crown Walk
Pioneer Square
Bicester, Oxfordshire
OX26 6HY, United Kingdom
It was the most impressive packaging that I have EVER SEEN!!! The books were in perfect condition!!!!!
Super fast delivery and well packaged. Quality item and service!