Ebook: Analytic Number Theory: Proceedings of a Conference in Honor of Paul T. Bateman

On April 25-27, 1989, over a hundred mathematicians, including eleven from abroad, gathered at the University of Illinois Conference Center at Allerton Park for a major conference on analytic number theory. The occa­ sion marked the seventieth birthday and impending (official) retirement of Paul T. Bateman, a prominent number theorist and member of the mathe­ matics faculty at the University of Illinois for almost forty years. For fifteen of these years, he served as head of the mathematics department. The conference featured a total of fifty-four talks, including ten in­ vited lectures by H. Delange, P. Erdos, H. Iwaniec, M. Knopp, M. Mendes France, H. L. Montgomery, C. Pomerance, W. Schmidt, H. Stark, and R. C. Vaughan. This volume represents the contents of thirty of these talks as well as two further contributions. The papers span a wide range of topics in number theory, with a majority in analytic number theory.

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Content:
Front Matter....Pages i-viii
q-Trinomial Coefficients and Rogers-Ramanujan Type Identities....Pages 1-11
Evaluations of Selberg Character Sums....Pages 13-21
Oscillations of Quadratic L-Functions....Pages 23-40
Elementary Proof of a Theorem of Bateman....Pages 41-46
The Prime k-Tuplets Conjecture on Average....Pages 47-75
On Arithmetic Functions Involving Consecutive Divisors....Pages 77-90
Small Zeros of Quadratic Forms Modulo p, II....Pages 91-94
Zeros of Derivatives Of the Riemann Zeta-Function Near the Critical Line....Pages 95-110
On some Exponential Sums....Pages 111-118
A Boundary Value Problem for a Pair of Differential Delay Equations Related to Sieve Theory, I....Pages 119-132
Some Remarks about Multiplicative Functions of Modulus < 1....Pages 133-157
On the Normal Behavior of the Iterates Of some Arithmetic Functions....Pages 159-164
On the Number of Partitions of n Without a Given Subsum, II....Pages 165-204
On Gaps between Squarefree Numbers....Pages 205-234
Some Arithmetical Semigroups....Pages 235-253
Norms in Arithmetic Progressions....Pages 255-264
Lower Bounds for Least Quadratic Non-Residues....Pages 265-268
Some Conjectures in Analytic Number Theory And their Connection With Fermat’s Last Theorem....Pages 269-309
Modular Integrals and Their Mellin Transforms....Pages 311-326
A Congruence for Generalized Frobenius Partitions with 3 Colors Modulo Powers of 3....Pages 327-342
The Coefficients of Cyclotomic Polynomials....Pages 343-348
The Rudin-Shapiro Sequence, Ising Chain, and Paperfolding....Pages 349-366
On Binomial Equations over Function Fields And a Conjecture of Siegel....Pages 367-382
Best Possible Results on the Density of Sumsets....Pages 383-393
Some Powers of The Euler Product....Pages 395-403
A Divergent Argument Concerning Hadamard Roots Of Rational Functions....Pages 405-411
Diagonalizing Eisenstein Series. I....Pages 413-427
Some Binary Partition Functions....Pages 429-450
On the Minimal Level of Modular Forms....Pages 451-477
Inequalities for Heights Of Algebraic Subspaces And the Thue-Siegel Principle....Pages 479-491
The Abstract Prime Number Theorem For Algebraic Function Fields....Pages 493-528
Back Matter....Pages 529-558
....Pages 559-560