A structure theorem in probabilistic number theory

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the distribution of an additive function on the integers, and its distribution on the primes.Comment: 10 page

Refinements of G\'al's theorem and applications

We give a simple proof of a well-known theorem of G\'al and of the recent related results of Aistleitner, Berkes and Seip [1] regarding the size of GCD sums. In fact, our method obtains the asymptotically sharp constant in G\'al's theorem, which is new. Our approach also gives a transparent explanation of the relationship between the maximal size of the Riemann zeta function on vertical lines and bounds on GCD sums; a point which was previously unclear. Furthermore we obtain sharp bounds on the spectral norm of GCD matrices which settles a question raised in [2]. We use bounds for the spectral norm to show that series formed out of dilates of periodic functions of bounded variation converge almost everywhere if the coefficients of the series are in $L^2 (\log\log 1/L)^{\gamma}$, with $\gamma > 2$. This was previously known with $\gamma >4$, and is known to fail for $\gamma<2$. We also develop a sharp Carleson-Hunt-type theorem for functions of bounded variations which settles another question raised in [1]. Finally we obtain almost sure bounds for partial sums of dilates of periodic functions of bounded variations improving [1]. This implies almost sure bounds for the discrepancy of $\{n_k x\}$ with $n_k$ an arbitrary growing sequences of integers.Comment: 16 page

Moments and distribution of central L-values of quadratic twists of elliptic curves

We show that if one can compute a little more than a particular moment for some family of L-functions, then one has upper bounds of the conjectured order of magnitude for all smaller (positive, real) moments and a one-sided central limit theorem holds. We illustrate our method for the family of quadratic twists of an elliptic curve, obtaining sharp upper bounds for all moments below the first. We also establish a one sided central limit theorem supporting a conjecture of Keating and Snaith. Our work leads to a conjecture on the distribution of the order of the Tate-Shafarevich group for rank zero quadratic twists of an elliptic curve, and establishes the upper bound part of this conjecture (assuming the Birch-Swinnerton-Dyer conjecture).Comment: 28 page

Future EMU Membership and Wage Flexibility in Selected EU Candidate Countries

This paper attempts to evaluate wage rigidity related to risks of increased size and volatility of unemployment after the candidate countries enter the EMU. Such evaluation is done through the study of past labour market adjustment mechanisms and, in particular, the role played by the exchange rate movements and independent monetary policy. The paper examines some institutional and structural characteristics of candidate countries labour markets that could influence the wage elasticity. The analysis indicates that generally nominal wages are not flexible in candidate countries. Inflationary surprises and nominal exchange rate movements have an effect on the adjustment, especially during the Russian crisis. On the other hand fast productivity growth creates the environment in which unit labour can adjust to unfavourable labour market outcomes through moderation of real wage dynamics despite nominal stickiness. The paper indicates possible fields of further in-depth research in this area.labour market, unemployment, European Monetary Union, EU enlargement, EMU enlargement, wage flexibility

Regional vs. Global Public Goods: The Case of Post-Communist Transition

The paper discusses the role of regional public goods vs. global goods in influencing postcommunist transition in Central and Eastern Europe and former USSR with special attention given to three particular factors: (i) external anchoring of national reform process; (ii) international trade arrangements and (iii) international financial stability. Our main finding is that that the EU, through the Eastern enlargement process, acted as the very effective regional public (club) good provider, whose influence across time and countries was correlated with better transition outcomes. In particular, the consolidation phase in democratization, institution building and structural transformation was successful in countries reforming under EU accession conditionality, but not under other forms of conditionality provided, for example, by the Bretton Woods institutions, . In the area of trade, gains from WTO accession were dwarfed by the impact of the opening of the EU trading block for accession countries. Finally, countries participating in EU integration showed more discipline in maintaining macroeconomic stability, while IMF programs were less effective in inducing stability in the absence of the European factor. This the main reason why CIS countries which got neither the EU accession perspective, nor even trade liberalization offer on the EU lag behind Central European, Baltic and Balkan countries in terms of democratization, rule of law, institutional stability and market-oriented economic reforms. However, due to observed ‘enlargement fatigue’ in the incumbent EU, the future attractiveness of the EU integration perspective and strength of the accessionassociated incentive system (in respect to countries of Western Balkans, CIS and Turkey) comes under question. There is also unclear whether European experience in providing regional public goods can be easily repeated in other geographic regions and to which extended can be used by the providers of global public goods.public goods, post-communist transition, European integration, trade liberalization, international financial stability