Squares in arithmetic progression with at most two terms omitted

Shanta Laishram; T. N. Shorey

Displaying similar documents to “Squares in arithmetic progression with at most two terms omitted”

Squares in products in arithmetic progression with at most one term omitted and common difference a prime power

Shanta Laishram, T. N. Shorey, Szabolcs Tengely (2008)

Acta Arithmetica

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The equation n(n+d) ⋯ (n+(k-1)d) = by² with ω(d) ≤ 6 or d ≤ 10¹⁰

Shanta Laishram, T. N. Shorey (2007)

Acta Arithmetica

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Almost squares in arithmetic progression (II)

Anirban Mukhopadhyay, T. N. Shorey (2003)

Acta Arithmetica

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Some extensions and refinements of a theorem of Sylvester

N. Saradha, T. N. Shorey, R. Tijdeman (2002)

Acta Arithmetica

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A note on arithmetic Diophantine series

Alexander E. Patkowski (2021)

Czechoslovak Mathematical Journal

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We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH. To accomplish this, Mellin inversion is applied to certain infinite series over arithmetic functions to apply Cauchy's residue theorem, and then the remainder of terms is estimated according to the assumption of the RH. In the last section, we use...