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6 results on '"Palojärvi, Neea"'

2. Conditional estimates for $L$-functions in the Selberg class

Author

Palojärvi, Neea and Simonič, Aleksander

Subjects
Mathematics - Number Theory, 11M06, 11M26, 41A30, FOS: Mathematics, Number Theory (math.NT)
Abstract

Assuming the Generalized Riemann Hypothesis, we provide upper bounds with explicit main terms for moduli of $\left(\mathcal{L}'/\mathcal{L}\right)(s)$ and $\log{\mathcal{L}(s)}$ for $|3/4-\sigma|\leq 1/4-\delta$, fixed $\delta\in(0,1/4)$ and for functions in the Selberg class. Moreover, by further assuming a polynomial Euler product representation for $\mathcal{L}(s)$, we establish uniform bounds in $\mathcal{L}$ for $|3/4-\sigma|\leq 1/4-1/\log{\log{\left(\mathrm{q}_{\mathcal{L}}|t|^{\mathrm{d}_{\mathcal{L}}}\right)}}$, $|1-\sigma|\leq 1/\log{\log{\left(\mathrm{q}_{\mathcal{L}}|t|^{\mathrm{d}_{\mathcal{L}}}\right)}}$ and $\sigma=1$, and completely explicit estimates by assuming also the strong $\lambda$-conjecture.

Published
2022

3. A p-adic lower bound for a linear form in logarithms.

Author

Palojärvi, Neea and Seppälä, Louna

Subjects
*LOGARITHMS, *RATIONAL numbers
Abstract

Linear forms in logarithms have an important role in the theory of Diophantine equations. In this paper, we prove explicit p -adic lower bounds for linear forms in p -adic logarithms of rational numbers using Padé approximations of the second kind. [ABSTRACT FROM AUTHOR]

Published
2023
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4. A $p$-adic lower bound for a linear form in logarithms

Author

Palojärvi, Neea and Seppälä, Louna

Subjects
Algebra and Number Theory, Mathematics - Number Theory, 11J61, Mathematics::Number Theory, FOS: Mathematics, Number Theory (math.NT)
Abstract

Linear forms in logarithms have an important role in the theory of Diophantine equations. In this article, we prove explicit $p$-adic lower bounds for linear forms in $p$-adic logarithms of rational numbers using Pad\'e approximations of the second kind., Comment: 27 pages

Published
2021

5. Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis.

Author

Ernvall-Hytönen, Anne-Maria and Palojärvi, Neea

Subjects
*RIEMANN hypothesis, *ARITHMETIC series
Abstract

We prove an explicit error term for the ψ (x,χ) function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions. [ABSTRACT FROM AUTHOR]

Published
2022
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6. EXPLICIT ZERO-FREE REGIONS AND A τ-LI-TYPE CRITERION.

Author

PALOJÄRVI, NEEA

Subjects
*RIEMANN hypothesis
Abstract

τ-Li coefficients describe if a function satisfies the Generalized Riemann Hypothesis or not. In this paper we prove that certain values of the τ-Li coefficients lead to existence or non-existence of certain zeros. The first main result gives explicit numbers N1 and N2 such that if all real parts of the τ-Li coefficients are non-negative for all indices between N1 and N2, then the function has non zeros outside a certain region. According to the second result, if some of the real parts of the τ-Li coefficients are negative for some index n between numbers n1 and n2, then there is at least one zero outside a certain region. [ABSTRACT FROM AUTHOR]

Published
2020
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