Bilinear sums with GL(2)$GL(2)$ coefficients and the exponent of distribution of d3$d_3$
Proceedings of the London Mathematical Society, Volume 128, Issue 3, March 2024.Abstract We obtain the exponent of distribution 1/2+1/30$1/2+1/30$ for the ternary divisor function d3$d_3$ to square‐free and prime power moduli, improving the previous results of Fouvry–Kowalski–Michel, Heath‐Brown and Friedlander–Iwaniec. The key input is certain estimates on bilinear sums with GL(2)$GL(2)$ coefficients obtained using the delta ...
Prahlad Sharma
wiley +1 more source
Riemann's Zeta Function and Prime Numbers : an approximation using von Mangoldt's explicit formula
, 2023 This essay aims to explain the connection between Riemann's zeta function and prime numbers. It relies heavily on Riemann's 1859 manuscript, in which he approximates the prime-counting function using the non-trivial zeros of the zeta function. The main result of this essay is von Mangoldt's explicit formula, which is a modified version of Riemann's ...
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From Grafts to Human Bioengineered Vascularized Skin Substitutes. [PDF]
Int J Mol Sci, 2020 Oualla-Bachiri W +3 more
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Liouville function, von Mangoldt function and norm forms at random binary forms
39 ...
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Pair correlation and twin primes revisited. [PDF]
Proc Math Phys Eng Sci, 2016 Conrey B, Keating JP.
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In this paper, we discuss an alternative approach to determine an asymptotic equivalent of the partial sum of the reciprocals of prime numbers. This well-known result, related to Merten's second theorem, is usually derived through methods similar to those found in Hardy and Wright's book ``An introduction to the theory of numbers'', involving ...
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Riemann hypothesis for period polynomials of modular forms. [PDF]
Proc Natl Acad Sci U S A, 2016 Jin S, Ma W, Ono K, Soundararajan K.
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The use of free osteoplasty together with trials on arthrodesis and joint transplantation. Archiv für klin Chirurgie. 1908;86(4):939-954. [PDF]
Clin Orthop Relat Res, 2008 Lexer E.
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The classic: Cartilaginous-cup arthroplasty in ununited fractures of the neck of the femur. 1948. [PDF]
Clin Orthop Relat Res, 2011 Moore JR.
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Artificial skin--culturing of different skin cell lines for generating an artificial skin substitute on cross-weaved spider silk fibres. [PDF]
PLoS One, 2011 Wendt H +7 more
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