Odd values of the Ramanujan $\tau $-function

M.Ram Murty; V.Kumar Murty; T.N. Shorey

Displaying similar documents to “Odd values of the Ramanujan $τ$ -function”

Some applications of Baker's sharpened bounds to diophantine equations

Robert Tijdeman (1974-1975)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

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On the greatest prime factor of $(a x^{m} + b y^{n})$

T. Shorey (1980)

Acta Arithmetica

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The equation $a x^{m} + b y^{m} = c x^{n} + d y^{n}$

T. Shorey (1982)

Acta Arithmetica

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Perfect powers in products of integers from a block of consecutive integers

T. Shorey (1987)

Acta Arithmetica

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Equal values of binary forms at integral points

Jan-Hendrik Evertse, Kalman Győry, T. Shorey, R. Tijdeman (1987)

Acta Arithmetica

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Lower bounds for the greatest prime factor of $a x^{m} + b y^{n}$

Yann Bugeaud (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

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The value of additive forms at prime arguments

Roger J. Cook (2001)

Journal de théorie des nombres de Bordeaux

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Let $f (𝐩)$ be an additive form of degree $k$ with $s$ prime variables $p_{1}, p_{2}, \dots, p_{s}$ . Suppose that $f$ has real coefficients $λ_{i}$ with at least one ratio $λ_{i} / λ_{j}$ algebraic and irrational. If s is large enough then $f$ takes values close to almost all members of any well-spaced sequence. This complements earlier work of Brüdern, Cook and Perelli (linear forms) and Cook and Fox (quadratic forms). The result is based on Hua’s Lemma and, for $k \geq 6$ , Heath-Brown’s improvement on Hua’s Lemma.

On the equation $y^{m} = P (x)$

Andrzej Schinzel, R. Tijdeman (1976)

Acta Arithmetica

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Displaying similar documents to “Odd values of the Ramanujan τ -function”

Displaying similar documents to “Odd values of the Ramanujan $τ$ -function”