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INDIAN INSTITUTE OF SCIENCE EDUCATION AND RESEARCH (IISER) PUNE
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An Autonomous Institution, Ministry of Human Resource Development, Govt. of India
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Seminars and Colloquia

Mathematics

Logarithmic mean values of multiplicative functions 
 
Tue, Oct 22, 2019,   04:00 PM to 05:00 PM at Madhava Hall

Dr. Akshaa Vatwani
IIT Gandhinagar

A general mean-value theorem for multiplicative functions taking values in the unit disc was given by Wirsing (1967) and Halász (1968). We consider a multiplicative function f belonging to a certain class of arithmetical functions and let F(s) be the associated Dirichlet series. In this setting, we obtain new Halász-type results for the logarithmic mean value of f. More precisely, we give estimates in terms of the size of $|F(1+1/\\log x)|$ and show that these estimates are sharp.  
As a consequence, we obtain a non-trivial zero-free region for partial sums of L-functions belonging to our class. We also report on some recent work showing that this zero free region is optimal. This is joint work with Arindam Roy.

    

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