Ebook: Analytic Number Theory and Diophantine Problems: Proceedings of a Conference at Oklahoma State University, 1984

A conference on Analytic Number Theory and Diophantine Problems was held from June 24 to July 3, 1984 at the Oklahoma State University in Stillwater. The conference was funded by the National Science Foundation, the College of Arts and Sciences and the Department of Mathematics at Oklahoma State University. The papers in this volume represent only a portion of the many talks given at the conference. The principal speakers were Professors E. Bombieri, P. X. Gallagher, D. Goldfeld, S. Graham, R. Greenberg, H. Halberstam, C. Hooley, H. Iwaniec, D. J. Lewis, D. W. Masser, H. L. Montgomery, A. Selberg, and R. C. Vaughan. Of these, Professors Bombieri, Goldfeld, Masser, and Vaughan gave three lectures each, while Professor Hooley gave two. Special sessions were also held and most participants gave talks of at least twenty minutes each. Prof. P. Sarnak was unable to attend but a paper based on his intended talk is included in this volume. We take this opportunity to thank all participants for their (enthusiastic) support for the conference. Judging from the response, it was deemed a success. As for this volume, I take responsibility for any typographical errors that may occur in the final print. I also apologize for the delay (which was due to the many problems incurred while retyping all the papers). A. special thanks to Dollee Walker for retyping the papers and to Prof. W. H. Jaco for his support, encouragement and hard work in bringing the idea of the conference to fruition.

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Content:
Front Matter....Pages i-ix
Multiplicative Functions and Small Divisors....Pages 1-13
Lectures on the Thue Principle....Pages 15-52
Polynomials with Low Height and Prescribed Vanishing....Pages 53-73
On Irregularities of Distribution and Approximate Evaluation of Certain Functions II....Pages 75-86
Simple Zeros of the Zeta-Function of a Quadratic Number Field, II....Pages 87-114
Differential Difference Equations Associated with Sieves....Pages 115-124
Primes in Arithmetic Progressions and Related Topics....Pages 125-134
Applications of Guinand’s Formula....Pages 135-157
Analytic Number Theory on GL(r,R)....Pages 159-182
Pair Correlation of Zeros and Primes in Short Intervals....Pages 183-203
One and Two Dimensional Exponential Sums....Pages 205-222
Non-Vanishing of Certain Values of L-Functions....Pages 223-235
On Averages of Exponential Sums over Primes....Pages 237-246
The Distribution of ?(n) among Numbers with No Large Prime Factors....Pages 247-281
On the Size of $sumlimits_{text{n} leqslant text{x}} {text{d(n)e(nx)}}$ ....Pages 283-290
Another Note on Baker’s Theorem....Pages 291-304
Sums of Polygonal Numbers....Pages 305-316
On the Density of B2-Bases....Pages 317-320
Statistical Properties of Eigenvalues of the Hecke Operators....Pages 321-331
Transcendence Theory Over Non-Local Fields....Pages 333-346
Back Matter....Pages 347-348

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Content:
Front Matter....Pages i-ix
Multiplicative Functions and Small Divisors....Pages 1-13
Lectures on the Thue Principle....Pages 15-52
Polynomials with Low Height and Prescribed Vanishing....Pages 53-73
On Irregularities of Distribution and Approximate Evaluation of Certain Functions II....Pages 75-86
Simple Zeros of the Zeta-Function of a Quadratic Number Field, II....Pages 87-114
Differential Difference Equations Associated with Sieves....Pages 115-124
Primes in Arithmetic Progressions and Related Topics....Pages 125-134
Applications of Guinand’s Formula....Pages 135-157
Analytic Number Theory on GL(r,R)....Pages 159-182
Pair Correlation of Zeros and Primes in Short Intervals....Pages 183-203
One and Two Dimensional Exponential Sums....Pages 205-222
Non-Vanishing of Certain Values of L-Functions....Pages 223-235
On Averages of Exponential Sums over Primes....Pages 237-246
The Distribution of ?(n) among Numbers with No Large Prime Factors....Pages 247-281
On the Size of $sumlimits_{text{n} leqslant text{x}} {text{d(n)e(nx)}}$ ....Pages 283-290
Another Note on Baker’s Theorem....Pages 291-304
Sums of Polygonal Numbers....Pages 305-316
On the Density of B2-Bases....Pages 317-320
Statistical Properties of Eigenvalues of the Hecke Operators....Pages 321-331
Transcendence Theory Over Non-Local Fields....Pages 333-346
Back Matter....Pages 347-348
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