On the frequency of titchmarsh’s phenomenon for ζ(s)—III

Balasubramanian, R.; Ramachandra, K.

doi:10.1007/bf03046849

Cited by 59 publications

(64 citation statements)

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“…Balasubramanian and Ramachandra [2] proved a similar result unconditionally, showing that there are arbitrarily large t such that…”

Section: Theorem 1 If T Is Sufficiently Large Then There Exists T ∈ [mentioning

confidence: 61%

“…Here denotes a smooth, non-negative function, compactly supported in [1,2], with (y) ≤ 1 for all y, and (y) = 1 for 5/4 ≤ y ≤ 7/4. Plainly max T ≤t≤2T…”

Section: Theorem 1 If T Is Sufficiently Large Then There Exists T ∈ [mentioning

confidence: 99%

“…Let be a smooth function compactly supported in [1,2], such that 0 ≤ (t) ≤ 1 always and (t) = 1 for t ∈ (5/4, 7/4). Letˆ (y) = ∞ −∞ (t)e −it y dt denote the Fourier transform of .…”

Section: Large Values Of ζ 1 + I T : Proof Of Theoremmentioning

confidence: 99%

“…Let L := √ log N log log N , and define f 2 ), and f ( p) = 0 for all other primes p. Note that the denominator in our ratio is…”

Section: Large Values Of ζ 1 + I T : Proof Of Theoremmentioning

confidence: 99%

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Extreme values of zeta and L-functions

2008

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“…Balasubramanian and Ramachandra [2] proved a similar result unconditionally, showing that there are arbitrarily large t such that…”

Section: Theorem 1 If T Is Sufficiently Large Then There Exists T ∈ [mentioning

confidence: 61%

“…Here denotes a smooth, non-negative function, compactly supported in [1,2], with (y) ≤ 1 for all y, and (y) = 1 for 5/4 ≤ y ≤ 7/4. Plainly max T ≤t≤2T…”

Section: Theorem 1 If T Is Sufficiently Large Then There Exists T ∈ [mentioning

confidence: 99%

Section: Large Values Of ζ 1 + I T : Proof Of Theoremmentioning

confidence: 99%

“…Let L := √ log N log log N , and define f 2 ), and f ( p) = 0 for all other primes p. Note that the denominator in our ratio is…”

Section: Large Values Of ζ 1 + I T : Proof Of Theoremmentioning

confidence: 99%

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Extreme values of zeta and L-functions

2008

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“…Dans le prolongement des travaux de Montgomery et Balasubramanian–Ramachandra , Bondarenko et Seip ont récemment obtenu — voir notamment [, ] — des bornes inférieures pour la quantité

Z_{β} false(T false) : = \underset{T^{β} ⩽ τ ⩽ T}{trueprefixmax} |ζ false(0false \frac{1}{2} + i τ false)| false(0 ⩽ β < 1, T ⩾ 1 false)

en minorant la norme de la forme quadratique associée à la sous‐somme

S (M)

. Leur approche repose sur la méthode de résonance, développée indépendamment, dans ce cadre, par Soundararajan et Hilberdink .…”

Section: Introduction Et éNoncé Des Résultatsunclassified

Sommes de Gál et applications

Bretèche

Tenenbaum

2018

Proc. London Math. Soc.

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We evaluate the asymptotic size of various sums of Gál type, in particular 0trueS(M):=∑m,n∈scriptM(m,n)[m,n],where scriptM is a finite set of integers. Elaborating on methods recently developed by Bondarenko and Seip, we obtain an asymptotic formula for log supfalse|scriptMfalse|=NS(M)/Nand derive new lower bounds for localized extreme values of the Riemann zeta‐function, for extremal values of some Dirichlet L‐functions at s=12, and for large character sums.

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