CHARACTER SUMS WITH EXPONENTIAL FUNCTIONS AND THEIR APPLICATIONS

By Y. MAVIM

CONTENTS PART ONE: PRELIMINARIES INTRODUCTION NOTATION AND AUXILIARY RESULTS PART TWO: BOUNDS OF CHARACTER SUMS BOUNDS OF LONG CHARACTER SUMS BOUNDS OF SHORT CHARACTER SUMS BOUNDS OF CHARACTER SUMS FOR ALMOST ALL MODULI BOUNDS OF GAUSSIAN SUMS PART THREE: MULTIPLICATIVE TRANSLATIONS OF SETS MULTIPLICATIVE TRANSLATIONS OF SUBGROUPS OF F? P MULTIPLICATIVE TRANSLATIONS OF ARBITRARY SETS MODULO P PART FOUR: APPLICATIONS TO ALGEBRAIC NUMBER FIELDS REPRESENTATIVES OF RESIDUE CLASSES CYCLOTOMIC FIELDS AND GAUSSIAN PERIODS PART ?VE: APPLICATIONS TO PSEUDO-RANDOM NUMBER GENERATORS PREDICTION OF PSEUDO-RANDOM NUMBER GENERATORS CONGRUENTIAL PSEUDO-RANDOM NUMBER GENERATORS PART SIX: APPLICATIONS TO FINITE FIELDS SMALL MTH ROOTS MODULO P SUPERSINGULAR HYPERELLIPTIC CURVES DISTRIBUTION OF POWERS OF PRIMITIVE ROOTS PART SEVEN: APPLICATIONS TO CODING THEORY AND COMBINATORICS DIFFERENCE SETS IN VP DIMENSION OF BCH CODES AN ENUMERATION PROBLEM IN FINITE FIELDS