Congruences for L-Functions: 511 (Mathematics and Its Applications, 511) - Softcover

Urbanowicz, J.; Williams, Kenneth S.

Softcover

ISBN 10: 9048154901 ISBN 13: 9789048154906

Publisher: Springer, 2010

Synopsis

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2. Their congruence provided a unified setting for many congruences proved previously by other authors using various means. The Hardy-Williams idea was as follows. Let d be the discriminant of a quadratic field. Suppose that d is odd and let d = PIP2· . . Pn be its unique decomposition into prime discriminants. Then, for any positive integer k coprime with d, the congruence holds trivially as each Legendre-Jacobi-Kronecker symbol (~) has the value + 1 or -1. Expanding this product gives ~ eld e:=l (mod4) where e runs through the positive and negative divisors of d and v (e) denotes the number of distinct prime factors of e. Summing this congruence for o < k < Idl/8, gcd(k, d) = 1, gives ~ (-It(e) ~ (~) =:O(mod2n). eld o

About this title

Review

This book is probably the most informative and highly helpful work on the subject of structural aspects of composites, and merits an honored place in the study of every student and researcher associated with composites. Practicing composite structures engineers dealing with composites cannot fail to find much of interest and motivate them in this volume. It demands a place in their libraries. Indeed a worthwhile investment that continues the level of excellence associated with the earlier edition. – Current Engineering Practice, vol. 47, 2004.

About the Author

Dr. Vinson is the H. Fletcher Brown Professor of Mechanical and Aerospace Engineering at the University of Delaware. In 1977 he received the ONR-AIAA Structural Mechanics Award for his research in composite materials, and in 1981 he was awarded an ASME Centennial Award. He is active as a consultant to government and industry. He recently received a Fellowship from the Japan Society for the Promotion of Science for 1985. He has been Chairman of the American Organizing Committee for the Japan-United States Conferences on Composite Materials three times (1981, 1983 and 1986). Dr. Sierakowski is Professor and Chairman of the Civil Engineering Department at the Ohio State University. He has held many academic and industrial posts in the United States and has been a National Research Council Senior Research Fellow, a consultant to Air Force Laboratories, and a Visiting Professor at the Air Force Office of Scientific Research.

Edition details

• Publisher: Springer
• Publication date: 2010
• Language: English
• ISBN 10: 9048154901
• ISBN 13: 9789048154906
• Binding: Paperback
• Number of pages: 268