# Analytic number theory in honor of helmut maier 12 birthday

On the representation of the number of integral points of an elliptic curve modulo a prime number , The Ramanujan Journal, Springer, 36 3 , — Yang On a multidimensional Hilbert-type integral inequality associated to the Gamma function , Applied Mathematics and Computation, , Yang On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function , Applied Mathematics and Computation, , — A cotangent sum related to zeros of the Estermann zeta function , Applied Mathematics and Computation, , — Popa On the stability of the linear functional equation in a single variable on complete metric groups , Journal of Global Optimization, 59 , — Jung On an n-dimensional mixed type additive and quadratic functional equation , Applied Mathematics and Computation, , 13— Yang A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function , Applied Mathematics and Computation, , — In collected volumes with B.

Yang A half-discrete Hardy-Hilbert-type inequality with a best possible constant factor related to the Hurwitz zeta function , In: In the Memory of Q.

### Various Number Theorists' Home Pages/Departmental listings

Rahman, Springer, , Maier Asymptotics and equidistribution of cotangent sums associated to the Estermann and Riemann zeta functions , In: From Arithmetic to Zeta-Functions. April 5, MathSciNet review: Let denote the sum of all of the positive divisors of , and let denote the sum of the proper divisors of.

First, we improve the upper and lower bounds for the counting function of numbers with deficient but abundant, or vice versa.

Second, we describe a heuristic argument suggesting the precise asymptotic density of not in the range of the function ; these are the so-called nonaliquot numbers. Finally, we prove new results on the distribution of friendly -sets, where a friendly -set is a collection of distinct integers which share the same value of. References [Enhancements On Off] What's this?

## Professor Glyn Harman

Additional Information Paul Pollack Affiliation: February 9, Received by editor s in revised form: January 4, Published electronically: April 5, Additional Notes: For Richard Guy on his 99th birthday.

May his sequence be unbounded. Alanen, Empirical study of aliquot sequences , Ph. Number Theory 9 , no.

## Kevin Ford's Reprints and Preprints

MR , https: Avidon , On the distribution of primitive abundant numbers , Acta Arith. Harman , Shifted primes without large prime factors , Acta Arith.

Bosma, Aliquot sequences with small starting values , preprint available from http: Catalan , Propositions et questions diverses , Bull. France 16 , — French.

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## Michael Th. Rassias

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