82 research outputs found
Bounding the Elliptic Mahler Measure
No full textWe give a simple inequality relating the elliptic Mahler measure of a polynomial to the traditional Mahler measure (via the length of the polynomial). These bounds are essentially sharp. We also give the corresponding result for polynomials in several variables. Keywords: Mahler measure, elliptic Mahler measure. AMS (1991) subject classification: Primary: 12D05; Secondary: 30C10, 11G05. Centre for Experimental and Constructive Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada & Department of Mathematics, University of British Columbia, Vancouver, BC V6 T 1Z2, Canada: [email protected]. 2 Chris Pinner 1 Introduction For a polynomial F (x) = d X i=0 a i x i = a d d Y i=1 (x \Gamma ff i ) 2 C[x] we recall the traditional Mahler measure of the polynomial M(F ) := ja d j d Y i=1 maxf1; jff i jg: (1) As observed by Mahler [6] this may be equivalently written in terms of an integral log M(F ) = Z 1 0 log jF (e 2ßit )jdt; (2) using Jensen's formula. Giv..
A Pleasant Conceyted Comedie of George a Greene, the Pinner of VVakefield.
No full textReproduces also the title-page of the Devonshire copy, with ms. notes, ascribing the authorship to Robet Greene.Label pasted on front end-paper reads: ... George-a-Greene the pinner of Wakefield, 1599. Date of earliest known edition, 1599 ... Reproduced in facsimile [Tudor facsimile texts] ... 1913.From the British museum copy (C. 34, b. 21)Mode of access: Internet
On Sums of Fractional Parts {nα+γ}
No full textAbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumCm(α, γ)=∑1⩽k⩽m({kα+γ}−12)whenαis irrational. From this we deduce a number of elementary bounds on the growth and behaviour ofCm(α, γ). In particular, we show that as m varies the extent of the fluctuations in size can be determined almost entirely from the non-homogeneous continued fraction expansion ofγwith respect toα. These sums are closely related to the discrepancy of the sequence ({nα}); we state a related explicit formula that yields similar bounds for the discrepancy. Sums of this form also occur in a lattice point problem of Hardy and Littlewood
The Lind-Lehmer Constant for cyclic groups of order less than 892,371,480
No full textWe determine the Lind–Lehmer constant for the cyclic group Zn when n is not a multiple of 892,371,480=2³⋅3⋅5⋅7⋅11⋅13⋅17⋅19⋅23
Chronicle (Paterson, NJ), Vol. 29, No. 43, Nov 3, 1957
No full textLocal information pertaining to Paterson, N.J. and surrounding Passaic County. Issues may include events, government, business, political cartoons, engagement and marriage announcements, and birth announcements. This publication was also known as the Paterson Chronicle (1952) and the Paterson Sunday Chronicle (1951-1952)
Chronicle (Paterson, NJ) Vol. 29, No. 44, Nov. 10, 1957
No full textLocal information pertaining to Paterson, N.J. and surrounding Passaic County. Issues may include events, government, business, political cartoons, engagement and marriage announcements, and birth announcements. This publication was also known as the Paterson Chronicle (1952) and the Paterson Sunday Chronicle (1951-1952)
Chronicle (Paterson, NJ), Vol. 29, No. 43, Oct. 27, 1957
No full textLocal information pertaining to Paterson, N.J. and surrounding Passaic County. Issues may include events, government, business, political cartoons, engagement and marriage announcements, and birth announcements. This publication was also known as the Paterson Chronicle (1952) and the Paterson Sunday Chronicle (1951-1952)
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