Lectures on mean values of the Reimann zeta function /
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| Author / Creator: | Ivić, A., 1949- |
|---|---|
| Imprint: | Berlin ; New York : Published for the Tata Institute of Fundamental Research [by] Springer-Verlag, c1991. |
| Description: | v, 363 p. ; 25 cm. |
| Language: | English |
| Series: | Lectures on mathematics and physics. Mathematics 82 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1487062 |
Table of Contents:
- Ch. I. Elementary Theory. 1.1. Basic properties of [zeta](s). 1.2. Elementary mean value theorems. 1.3. Bounds over short intervals. 1.4. Lower bounds for mean values over short intervals
- Ch. II. The Error Terms in Mean Square Formulas. 2.1. The mean square formulas. 2.2. The beginning of proof. 2.3. Transformation of the expressions for the error terms. 2.4. Evaluation of some exponential integrals. 2.5. Completion of the proof of the mean square formulas. 2.6. The mean square formula for E(T). 2.7. The upper bounds for the error terms. 2.8. Asymptotic mean square of the product of the zeta-function and a Dirichlet polynomial
- Ch. III. The Integrals of the Error Terms in Mean Square Formulas. 3.1. The formulas for the integrated error terms. 3.2. The omega-results. 3.3. The mean square formulas. 3.4. The zeros of E(T) - [pi]. 3.5. Some other results
- Ch. IV. A General Study of Even Moments. 4.1. The error term for the 2k-th moment. 4.2. The approximate functional equation. 4.3. Evaluation of I[subscript k](T). 4.4. Evaluation of the first main term. 4.5. The mean square formula. 4.6. The fourth power moment. 4.7. The sixth power moment
- Ch. V. Motohashi's Formula for the Fourth Moment. 5.1. Introduction and statement of results. 5.2. Analytic continuation. 5.3. Application of spectral theory and Kuznetsov's trace formula. 5.4. Further analytic continuation and the explicit formula. 5.5. Deductions from the explicit formula. 5.6. Upper bounds. 5.7. The omega-result
- Ch. VI. Fractional Mean Values. 6.1. Upper and lower bounds for fractional mean values. 6.2. An asymptotic formula for mean values. 6.3. The value distribution on the critical line. 6.4. Mean values over short intervals.
