دانلود کتاب Exponential Sums and Their Applications

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Cover......Page 1
Series Editors......Page 2
Title: Exponential Sums and their Applications......Page 3
ISBN 0-7923·-1647-9......Page 4
Series Editor's Preface......Page 6
CONTENT'S......Page 8
PREFACE......Page 10
INTRODUCTION......Page 12
§ 1. Sums of the first degree......Page 18
§ 2. General properties of complete sums......Page 0
§ 3. Gaussian sums......Page 30
§ 4. Simplest complete sums......Page 39
§ 5. Mordell's method......Page 46
§ 6. Systems of congruences......Page 51
§ 7. Sums with exponential function......Page 57
§ 8. Distribution of digits in complete period of periodic fractions......Page 62
§ 9. Exponential sums with recurrent function......Page 70
§ 10. Sums of Legendre's symbols......Page 78
§ 11. Weyl's method......Page 85
§ 12. Systems of equations......Page 95
§ 13. Vlnogradov's mean value theorem......Page 104
§ 14. Estimates of Weyl's sums......Page 114
§ 15. Repeated applicatioll of the mean value theorem......Page 127
§ 16. Sums arising in zeta-function theory......Page 136
§ 17. Incomplete rational sums......Page 143
§ 18. Double exponential sums......Page 150
§ 19. Uniform distribution of fractional parts......Page 156
§ 20. Uni,form distribution of functions systems and completely uniform distribution......Page 166
§ 21. Normal and conjunctly normal numbers......Page 176
§ 22. Distribution of digits in period part of periodical fractions......Page 183
§ 23. Connection between exponential sums, quadrature formulas and fractional parts distribution......Page 193
§ 24. Quadrature and interpolation formulas with the number-theoretical nets......Page 204
REFERENCES......Page 220
SUBJ'ECT INDEX......Page 224
IN'DEX OF NAMES......Page 226
Back Cover......Page 227