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Let N(a, m) be the least integer n (if exists) such that φ(n) ≡ a (mod m). Friedlander and Shparlinski proved that for any ε > 0 there exists A = A(ε) > 0 such that for any positive integer m which has no prime divisors p < (log m) and any integer a with gcd(a,m) = 1, we have the bound N(a,m) ¿ m. In the present paper we improve this bound to N(a,m) ¿ m.

In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor–Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. T...

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under the assumption of the product structure near boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dir...

Lawrence, N., Martin, A., Toner, G., Stockler, M., Buizen, L., Thomson, D., Gebski, V., Friedlander, M., Yeung, A., Wong, N., Grimison, P., et al (2016). Long-term outcomes of accelerated BEP (bleomycin, etoposide, cisplatin) for advanced germ cell tumours: updated analysis of an Australian multicenter phase II trial by the Australian and New Zealand Urogenital and Prostate Cancer Trials Group ...

This paper examines percolation questions in a deterministic setting. In particular, I consider R, the set of elements of Z2 with greatest common divisor equal to 1, where two sites are connected if they are at distance 1. The main result of the paper proves that the infinite component has an asymptotic density. An “almost everywhere” sieve of J. Friedlander is used to obtain the result.

In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor–Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. T...

Introduction 2 1. Symmetric spectra 5 1.1. Simplicial sets 5 1.2. Symmetric spectra 6 1.3. Simplicial structure on Sp 8 1.4. Symmetric Ω-spectra 10 2. The smash product of symmetric spectra 11 2.1. Symmetric sequences 11 2.2. Symmetric spectra 14 2.3. The ordinary category of spectra 18 3. Stable homotopy theory of symmetric spectra 19 3.1. Stable equivalence 20 3.2. Model categories 26 3.3. Le...