Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Long-Lasting Bank Relationships and Growth of Firms Abstract A puzzling but consistent result in the empirical literature on banking is that firms with close bank ties do not grow faster than bank-independent firms. In this paper, we reconsider the link between relationship lending and firms' growth, distinguishing firms by size and "health". The idea is that the beneficial effects of relationship lending on information asymmetries can be compensated by other negative capture, risk and externality effects which make relational banks reluctant to support long-term growth projects of client firms, and that the strength of these compensating effects varies with firm size and health status. We explore the influence of long-lasting bank relationships on employment and asset growth of a large sample of Italian firms. The main finding is that relationship lending hampers the efforts of small firms to increase their size, while it mitigates the negative growth of troubled, medium-large enterprises. Terms of use: Documents inJEL-Code: G21, G34.Keywords: relationship lending, capture effects, firms' growth. We wish to thank Piero Alessandrini, Carlo Altavilla, Marco Lilla, Jack Lucchetti, Lars Norden, Andrea Presbitero, Franco Spinelli, Carmine Trecroci and Timo Wollmershäuser for comments and suggestions. Our thanks also go to seminar participants at the University of Brescia, University of Naples 'Parthenope', University of Milan and at the MoFiR conference on The changing geography of money, banking and finance in a post-crisis world (Ancona, Italy) and the Cesifo-Delphi conference on Financial markets, corporate governance and macroeconomic outcomes (Munich, Germany). Usual disclaimer applies. Alessandro Gambini 2

We investigate the average number of representations of a positive integer as the sum of k + 1 perfect k-th powers of primes. We extend recent results of Languasco and the last Author, which dealt with the case k = 2 [6] and k = 3 [5] respectively. We use the same technique to study the corresponding problem for sums of just k perfect k-th powers of primes.

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