000			01631nam a2200265Ia 4500
008			160627s2012||||xx |||||||||||||| ||und||
080			_aHBNI Th52
100			_aKrishnan Rajkumar _eauthor
245			_aZeros of general L-functions on the critical line
260			_c2012
300			_a65p.
502			_a2012
502			_bPh.D
502			_cHBNI
520	3		_aThe author studies the gaps between consecutive zeros on the critical line for the Riemann zeta function, and some of its generalisations, namely, the Epstein zeta function and the Selberg class of functions. First a simplified exposition of a result of Ivic and Jutila on the large gaps between consecutive zeros of Riemann zeta function on the critical line is given. Then presented a generalisation of this result to the case of the Epstein zeta function associated to a certain binary, positive definite, integral quadratic form Q(x, y). Then established the analogue of Hardy's theorem, namely, - that there are infinitely many zeros on the critical line, for degree 2 elements of the Selberg class of L-functions whose Dirichlet coefficients satisfy certain mild growth conditions. The study concludes with a conditional version of Hardy's theorem for the degree d > 2 elements of the Selberg class.
650	1	4	_aMathematics
653	1	0	_aEpstein Zeta Function
653	1	0	_aHBNI Th52
653	1	0	_aRiemann Zeta Function
653	1	0	_aSelberg Class
720	1		_aSrinivas, K. _eThesis advisor [ths]
856			_uhttp://www.imsc.res.in/xmlui/handle/123456789/339
942			_2THESIS149 _cTHESIS
999			_c48854 _d48854