Conjectures in Arithmetic Algebraic Geometry: A Survey by Wilfred W.J. Hulsberge

Description: Conjectures in Arithmetic Algebraic Geometry: A Survey by Wilfred W.J. Hulsbergen Estimated delivery 3-12 business days Format Paperback Condition Brand New Description In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermats Last Theorem one is naturally led to introÂ duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermats Last Theorem for a large class of exponents. Before Kummer, DirichÂ let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemanns paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by properÂ ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theoristss view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlets L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generalizaÂ tion of Dirichlets L-functions with a generalization of class field theÂ ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number th Publisher Description In this expository paper we sketch some interrelations between several famous conjectures in number theory and algebraic geometry that have intrigued mathematicians for a long period of time. Starting from Fermats Last Theorem one is naturally led to intro duce L-functions, the main motivation being the calculation of class numbers. In particular, Kummer showed that the class numbers of cyclotomic fields playa decisive role in the corroboration of Fermats Last Theorem for a large class of exponents. Before Kummer, Dirich let had already successfully applied his L-functions to the proof of the theorem on arithmetic progressions. Another prominent appearance of an L-function is Riemanns paper where the now famous Riemann Hypothesis was stated. In short, nineteenth century number theory showed that much, if not all, of number theory is reflected by proper ties of L-functions. Twentieth century number theory, class field theory and algebraic geometry only strengthen the nineteenth century number theoristss view. We just mention the work of E. Heeke, E. Artin, A. Weil and A. Grothendieck with his collaborators. Heeke generalized Dirichlets L-functions to obtain results on the distribution of primes in number fields. Artin introduced his L-functions as a non-abelian generaliza tion of Dirichlets L-functions with a generalization of class field the ory to non-abelian Galois extensions of number fields in mind. Weil introduced his zeta-function for varieties over finite fields in relation to a problem in number theory. Details ISBN 3528064331 ISBN-13 9783528064334 Title Conjectures in Arithmetic Algebraic Geometry: A Survey Author Wilfred W.J. Hulsbergen Format Paperback Year 1992 Pages 240 Publisher Vieweg+teubner Verlag GE_Item_ID:140396117; About Us Grand Eagle Retail is the ideal place for all your shopping needs! With fast shipping, low prices, friendly service and over 1,000,000 in stock items - you're bound to find what you want, at a price you'll love! Shipping & Delivery Times Shipping is FREE to any address in USA. Please view eBay estimated delivery times at the top of the listing. Deliveries are made by either USPS or Courier. We are unable to deliver faster than stated. International deliveries will take 1-6 weeks. NOTE: We are unable to offer combined shipping for multiple items purchased. This is because our items are shipped from different locations. Returns If you wish to return an item, please consult our Returns Policy as below: Please contact Customer Services and request "Return Authorisation" before you send your item back to us. Unauthorised returns will not be accepted. Returns must be postmarked within 4 business days of authorisation and must be in resellable condition. Returns are shipped at the customer's risk. We cannot take responsibility for items which are lost or damaged in transit. For purchases where a shipping charge was paid, there will be no refund of the original shipping charge. Additional Questions If you have any questions please feel free to Contact Us. Categories Baby Books Electronics Fashion Games Health & Beauty Home, Garden & Pets Movies Music Sports & Outdoors Toys

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