DORIN GHISA Riemann Zeta function is one of the most studied transcendental functions, having in view its many applications in number theory,algebra, complex analysis, statistics, as well as in physics. Another reason why this function has drawn so much attention is the celebrated Riemann conjecture regarding its non trivial zeros, which resisted proof or disproof until now. There has been lately a lot of progress in the sense of proving its truthfulness.

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The Riemann zeta function

In this window, all groups are assumed finite. Here we collect a number of results that play a significant role in the book (further material of an elementary nature that we sometimes take for granted is easily available in textbooks such as [H], [R] and [A]).

Finite Group Theory

A. Dedekind Sums

Multiplicative Number Theory I: Zeros

The Hardy–Littlewood method: Bibliography

On the average value of the least common multiple of k positive integers

A unitary analogue of Pillai’s arithmetical function is introduced, and an asymptotic formula is proved.

The unitary analogue of Pillai's arithmetical function

Let ℤm be the group of residue classes modulo m. Let s(m, n) denote the total number of subgroups of the group ℤm × ℤn, where m and n are arbitrary positive integers. We derive asymptotic formulas for the sum ∑m,n≤x s(m, n) and for the corresponding sum restricted to gcd(m, n) > 1 which concerns the groups ℤm × ℤn having rank two.

ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤm × ℤn

Let $N_k(n,r,\boldsymbol{a})$ denote the number of incongruent solutions of the quadratic congruence $a_1x_1^2+\ldots+a_kx_k^2\equiv n$ (mod $r$), where $\boldsymbol{a}=(a_1,\ldots,a_k)\in {\Bbb Z}^k$, $n\in {\Bbb Z}$, $r\in {\Bbb N}$. We give short direct proofs for certain less known compact formulas on $N_k(n,r,\boldsymbol{a})$, valid for $r$ odd, which go back to the work of Minkowski, Bachmann and Cohen. We also deduce some other related identities and asymptotic formulas which do not seem to appear in the literature.

Counting solutions of quadratic congruences in several variables revisited

Universal hashing, discovered by Carter and Wegman in 1979, has many important applications in computer science. MMH∗, which was shown to be Δ-universal by Halevi and Krawczyk in 1997, is a well-kn...

László Tóth

Papers

On the average value of the least common multiple of k positive integers

The unitary analogue of Pillai's arithmetical function

ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤm × ℤn

Counting solutions of quadratic congruences in several variables revisited

On an Almost-Universal Hash Function Family with Applications to Authentication and Secrecy Codes