ABSTRACT ANALYTIC NUMBER THEORY

By N. KUNAS

CONTENTS PART I ANALYTIC NUMBER THEORY, COMBINATORICS, AND SPECIAL SEQUENCES OF NUMBERS AND POLYNOMIALS THE MEAN VALUES OF THE RIEMANN ZETA-FUNCTION ON THE CRITICAL LINE EXPLICIT BOUNDS CONCERNING NON-TRIVIAL ZEROS OF THE RIEMANN ZETA FUNCTION ON THE VALUE-DISTRIBUTION OF LOGARITHMIC DERIVATIVES OF DIRICHLET L-FUNCTIONS MULTIPLE GAMMA FUNCTIONS AND THEIR APPLICATIONS ON PARTITION FUNCTIONS OF HYPERBOLIC THREE-GEOMETRY AND ASSOCIATED HILBERT SCHEMES FAMILIES OF TWISTED BERNOULLI NUMBERS, TWISTED BERNOULLI POLYNOMIALS, AND THEIR APPLICATIONS COMBINATORIAL INTERPRETATION OF A GENERALIZED BASIC SERIES IDENTITIES FOR RECIPROCAL BINOMIALS A NOTE ON Q-STIRLING NUMBERS PART II ANALYTIC INEQUALITIES AND APPLICATIONS A SURVEY ON CAUCHY–BUNYAKOVSKY–SCHWARZ INEQUALITY FOR POWER SERIES TOPICS IN SPECIAL FUNCTIONS III COMPLETELY MONOTONE FUNCTIONS: A DIGEST NEW APPLICATIONS OF SUPERQUADRACITY GREEN’S OPERATOR AND DIFFERENTIAL FORMS MULTIDIMENSIONAL DISCRETE HILBERT-TYPE INEQUALITIES, OPERATORS AND COMPOSITIONS THE FUNCTION BX AX/=X BX AX/=X BX AX/=X: RATIO’S PROPERTIES ON THE APPROXIMATION AND BOUNDS OF THE GINI MEAN DIFFERENCE ON PARAMETRIC NONCONVEX VARIATIONAL INEQUALITIES PART III APPROXIMATION OF FUNCTIONS AND QUADRATURES SIMULTANEOUS APPROXIMATION FOR STANCU-TYPE GENERALIZATION OF CERTAIN SUMMATION–INTEGRAL-TYPE OPERATORS KOROVKIN-TYPE APPROXIMATION THEOREM FOR FUNCTIONS OF TWO VARIABLES VIA STATISTICAL SUMMABILITY C; 1; 1/ RE?ECTIONS ON THE BAKER–GAMMEL–WILLS (PADÉ) CONJECTURE OPTIMAL QUADRATURE FORMULAS AND INTERPOLATION SPLINES MINIMIZING THE SEMI-NORM IN THE HILBERT SPACE K2 P2/ NUMERICAL INTEGRATION OF HIGHLY OSCILLATING FUNCTIONS PART IV ORTHOGONALITY, TRANSFORMATIONS, AND APPLICATIONS ASYMPTOTIC REDUCTIONS BETWEEN THE WILSON POLYNOMIALS AND THE LOWER LEVEL POLYNOMIALS OF THE ASKEY SCHEME ON A DIRECT UVAROV-CHIHARA PROBLEM AND SOME EXTENSIONS ON ESPECIAL CASES OF BOAS-BUCK-TYPE POLYNOMIAL SEQUENCES GOURSAT’S HYPERGEOMETRIC TRANSFORMATIONS, REVISITED CONVOLUTION PRODUCT AND DIFFERENTIAL AND INTEGRO: DIFFERENTIAL EQUATIONS ORTHOGONALLY ADDITIVE: ADDITIVE FUNCTIONAL EQUATION