On Linnik's constant

Graham, S. W.

doi:10.4064/aa-39-2-163-179

Cited by 41 publications

(32 citation statements)

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“…Using Burgess' estimate, Graham [7] improved the exponent 2 to 3/2 for bounded t. Later, using Heath-Brown's estimate (cf. (3.2) in the next section), W. Wang showed essentially [17] (2.24)…”

Section: Theorem 2 Under the Conditions Of Theorem 1 Formentioning

confidence: 99%

Some new density theorems for Dirichlet $L$-functions

Pintz¹

2019

Banach Center Publ.

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Section: Theorem 2 Under the Conditions Of Theorem 1 Formentioning

confidence: 99%

Some new density theorems for Dirichlet $L$-functions

Pintz¹

2019

Banach Center Publ.

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“…The method we employ in this section is based on the work of Graham and Jutila on computing explicit Linnik constants (see [4,7]) as well as that of Kaufman (see [8]). …”

Section: Proof Of Theorem 11mentioning

confidence: 99%

“…In particular, the bound no longer depends on the length β − α of the interval I. 1 The kernel, as defined in §7 of [4] is missing a factor of s in the denominator. We have corrected the kernel in our definition of K(s).…”

Section: Completing the Proofmentioning

confidence: 99%

Linnik’s theorem for Sato-Tate laws on elliptic curves with complex multiplication

Chen

Park

Swaminathan³

2015

Res. number theory

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Let E/Q be an elliptic curve with complex multiplication (CM), and for each prime p of good reduction, let a E (p) = p + 1 − #E(F p ) denote the trace of Frobenius. By theIn this paper, we prove that the least prime p such thatwhere N E is the conductor of E and the implied constant and exponent A > 2 are absolute and effectively computable. Our result is an analogue for CM elliptic curves of Linnik's Theorem for arithmetic progressions, which states that the least prime p ≡ a (mod q) for (a, q) = 1 satisfies p q L for an absolute constant L > 0.

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“…This allows to get wider zero-free region for ζ(s): in particular, Rosser and Schoenfeld obtained R 0 = 9.645908801 in [15]. For more detail see Stechkin [16], Rosser and Schoenfeld [15], and Graham [4].…”

Section: Combining This Bound Andmentioning

confidence: 99%